What a lot of fans don't seem to get is that it is all about personality types, not functional specialties, or political recruiting. Girls are "recruited" for Ajahs based on the perception that they will fit in with the rest of the club. There might be SOME competition for girls who could go either way, but there doesn't seem to be any political advantage to having a larger Ajah, all seven being equally represented in the Hall, and thus the political process. There are no popular referendums or votes that affect anything outside of an Ajah, so really, all that increasing the number of sisters in your Ajah does, is dilute the effect of your vote for Sitter or First Whatever, as well as increase the competition for those positions. When they were both raised to full sisters, Seaine had a much easier road to the Hall than did Pevara.

Actually, I don't get the impression anyone really knows much about the Ajahs. Aes Sedai especially seem to be more inclined to quell any though of an outsider judging or making distinctions among the sisters: as far as anyone else is concerned, they are ALL Aes Sedai, and that's all anyone needs to know. They don't WANT people favoring one Ajah or another, or judging any sister by any criteria other than possession of shawl and ring. Until the Wondergirls start getting deeper into their training, even the readers don't know much about the differences. We had no idea what the Greens were all about, or why they had so many Warders, until Egwene asked Alanna in tDR (something she and Elayne both failed to pick up throughout their entire novitiate). That said, fighting supernatural threats DOES seem to be the most obvious notions to occur to people signing up for such an organization, even if they don't know exactly who does it. We would have thought Auror was a cool job in the Potterverse even if we never knew there was a word for it.

Anyway, it seems that in WoT, women adhere rather closely to a number of common generalizations, many of which I have heard expressed in the real world as well. Even the differences in saidar & saidin reflect this, as do the distribution of the Five Powers, and the mechanics of linking.

One of the perceived differences between men and women is that men tend more to abstract loyalties and ideals, while women tend to more visceral, immediate and personal loyalties and priorities. According to this worldview, a woman might fight as fiercely as a man, but in the manner of a she-bear defending her cubs, instead of for a flag or a slogan. Such women merely transpose the subject of feminine ferocity to a nation or a political agenda or whatever.

Note that both of the combat Ajahs are focused on defense and countering threats: the archetypal feminine priority of security. And they link methods with personalities: the Greens are militaristic, while the Reds are more like LEOs. Although the initial impression of the Greens was highly sexualized, later sources assert that most Aes Sedai-Warder relationships are chaste. Elayne notes as much as well, that her early interest in the Warder bond was based on adolescent romanticizing situations which were nothing of the sort. And even the first impressions of the Greens support this view, rather than a retcon: the first observed difference by a PoV character is that on the road from Fal Dara to the ship for Tar Valon, the Greens are up late every night talking cheerfully with their warders at their campfire. If they were actually the nymphos of reputation, they would have been in the tents getting it on. That is the reality of Greens vis a vis men: they like their company, and get into masculine type stuff (being one of the largest Ajahs, they are also much less likely to be of a personality type). They need that, because they have to accompany armies. They COUNTER the Dreadlords with the Shadow's forces, they don't do the fighting themselves. For that you need troops. So that's why Alanna says you have to love men. Even Cadsuane, for all that she seems to be a 300 year old virgin from one of the most notoriously misandrist societies in WoT, has compassion and understanding for men where few other people in the entire world do. Her behavior after Rand is wounded by Fain is the most telling example of this, I think. How many other sisters would have heeded Min's admonition about his reaction to waking up surrounded by strange Aes Sedai. Cadsuane is not the sort to slack on security, so she could not have seriously been afraid of what he might do. The only explanation, which fits with her promise to her unconscious charge, is that she is concerned about the psychological harm it might do Rand, and that she wants to spare him that.

So even though they are entirely feminine in manner and reputation, the Greens like men. The Reds, on the other hand, resent and suspect them, like cops do minorities. Yet, while they might not have the strict military-inspired hierarchies of the Greens, they appear to match their "opposites" in discipline and control and the authority granted their Ajah Head. What's more, they, more than any other Ajah, seem to maintain an "us against the world" mentality, which probably reinforces how the Ajah with the largest population, tends to adhere most closely to its stereotypes. There should be more atypical Reds than other Ajahs, but they seem to be more universally hardassed than the rest. Even the more humanized ones like Tarna, Pevara and Silviana could at the mildest be called "tough but fair".

And these are the stereotypes of women in masculine pursuits or authority positions. One of the boys, or a battleaxe. Reveling in their feminine distinctions, or rejecting masculinity altogether (as the epitome of symbolic womanhood, there is no role in the story for an Aes Sedai who rejects femininity or embraces masculinity, much less a whole Ajah of them - even the most homosexual Aes Sedai we see, Galina, is femme & not butch), but they are both unquestionably female archetypal personalities, for all they are supposed opposites. And they are the largest Ajahs, because in WoT, male and female have been forced into opposition by the Shadow, when they are supposed to be working together.

The Blues and Whites are the smallest, because ideals and logic are both aspects of abstract thinking, which is a masculine archetype. In between are the Yellows, with their nurturing, and the Grays with their conciliation and peace-making. The scholasticism of the Browns is not a typical female role, but hardly avoidable given the fantasy archetypes of the magical scholar, not to mention the scholastic experience of the PoV characters who are our window inside the Tower. I think even if there was no Shadow threat or taint, the Greens and Reds would still be pretty big, but would have different focuses. Maybe take that investigative and law enforcement thing Beonin seems into from the Grays. But they would still be considerable in number, because their personality types are so important in the spectrum of female activity. They are the two most involved with men, and a key aspect of the WoT ethos is that while they are distinct and discrete by necessity, the genders must work together. Functional societies in WoT have specific roles, and especially authority positions, for each sex. Many different lands show similar perceptions of what is male and what is female, such as the respective spheres of influence of the First Prince of the Sword in Andor, and the Master of Blades among the Sea Folk, and even the King of Tarabon in contrast with the Panarch. Men and women have to work together, so it stands to reason that the two most important personality types for women are those geared toward dealing with men, one way or another. Not to mention the feedback mechanism by which balance is maintained in WoT would have two such contrasting types of approach to dealing with men. The affection & acceptance of the Greens is balanced by the wariness & scrutiny of the Reds. The other Ajah personality types would represent the sorts of women who can take or leave men, or have then in their lives on specific terms (family members/Warders), but whose lives are not ABOUT men. If they have careers, they are technical or traditionally feminine, as opposed to say, military or business or skilled heavy labor (which are the types of women who join the Green or Red).

I think that women who are not members of an Ajah are not good judges of whether or not a peer would fit. Seaine thinks Pevara would make a good Green, but how much does she know about what goes on in the Green OR Red Ajahs? If Pevara is not a great Red, how did she become a Sitter? She might have a different view of the Ajah's methods, and odd tastes, but that doesn't necessarily exclude her from what makes a really good Red. Egwene, superficially, would be a great Red, because she has no real positive or affirming relations with any men. She is a constant critic and always in an adversarial position with the men in her life, even Gawyn. But her actions, she would seem to hate them. From her first appearance, to his last thought about her, Rand is always on target about her opinions or reactions, and feels compelled to ask her not to pick the Red. But Egwene and the Greens don't think so.

Functionally speaking, there is a lot of overlap between Ajahs. Alanna says as much when describing what the Greens do. She is a better Healer than Verin, Cadsuane hunts men better than any Red (and some readers have accused her of having typical Red attitudes towards men), Elayne is a superb diplomat, Vandene is as learned as a Brown, and Egwene as devoted to her cause as any Blue.

The Blues range in Healing ability from Moiraine, who is excellent, to Sheriam, who is Egwene's touchstone example of an Aes Sedai who can't do it. They have field agents like Moiraine, and bureaucrats like Siuan.

From the other end, a lot of sisters we see could do well at more than one Ajah's function, as you seem to be pointing out. By the metric of the specializations, Cadsuane could be a Red, she concentrates on causes like a Blue, and however atypical her methods, is as effective a diplomat as a Gray. Moiraine is enough of a soldier and warrior to impress the Borderlanders (and seems to have spent as much time along the Blightborder as many Greens her age), she is a good Healer, and by quantity over quality, blows any Red out of the water at male channeler hunting with her single find. I don't see much indication that the average Yellow would have done much better at the common form of Healing. Elayne is credited with sufficient political acumen to impress Blue sitters, she is diplomatic (and legal-minded) enough for a Gray, and her reverse engineering talents could probably find a scholastic outlet. She is the most "head over heart" thinker of any major female character, and with the right philosophical training could do well in the Whites. I don't think anyone doubts Nynaeve could do just as well in the Green as the Yellow or even the Red, given her quirky intuitive methods of reading people and figuring things out. She passionate enough to get into causes, and had experience sitting in judgement that she might make a good Gray. Egwene could do Blue or Red, as mentioned above, though I don't think she'd make a good Brown or White, and she's too abrasive and flexible for a Gray, but she would be an acceptable Yellow, if you swallow Suana's Sandersonian formulation. By that token, Verin, Cadsuane and Elayne would make good Yellows, too.

Anyway, my point is that while functionally, a given woman might be good for many different Ajahs on paper, I think it's really a matter of personalities and thought process, and how you get along with certain types of people. Nynaeve would not get along with the Green hierarchy ( "other people...made stupid rules" ), Egwene would let herself be diverted from pursuit of a channeler or her cause, for another one, Elayne would be too much more interested in the results instead of the process for Tower politics or negotiating treaties. Elayne is a fighter, who works well within hierarchies and goes after enemies without counting the cost or risks. That makes her a Green, not skill specialization. Egwene shares those traits to a large degree, and that's pretty much what the two of them have in common. Whatever other traits and skills Nynaeve has in her arsenal, her focus, from the first time she channeled through the end of the series, has always been about healing. Even her momentary fixation on avenging the mess Moiraine made of the Two Rivers folks' lives was in a misguided belief that it would somehow fix what Moiraine did to them. Her insights and abilities to figure stuff out could be a form of diagnostic talent.

I doubt that's a unique Blue philosophy. They don't care about what other Ajahs care about, so to them it doesn't look like the others are making good use of their people, but what do they really know about what the others want?

Moiraine might show a variety of interests and Ajah talents, but they are all in service to her cause. She does or becomes whatever she has to in order to serve that cause. Even rejecting a life of politics, the supposed main skill of her chosen Ajah.

I don't think the Blues are necessarily politicians, they are idealists and activists, and it is an indicator of the current state of the Tower that idealism and activism translates into political scheming and power games. The political focus is hardly unique to that Ajah, either. How many Yellows do we see running around the world looking to Heal? All of them seem far more oriented toward the Tower than might be expected, and only the Reds have the excuse of being on top of things, what with the world remaining unbroken for three thousand years, and even RJ giving them credit for being so effective at hunting men that they have culled the trait from the population. Every other Ajah's chosen specialization seems to have a negligible effect on the world, except maybe the Whites, who explicitly don't care. What matters in choice of Ajah is how and why you use whatever skills, regardless of with which Ajah they are generally associated.