There's a similar logic behind opening schools and universities. The Brown Ajah would love it. I really think it just hasn't occurred to them.
The Servants of All never think about ways to be of service. They promote the Tower so much in their minds, that they have a hard time thinking of anything else as important, even if they might be generally inclined to be helpful or a positive influence.
Another issue is that even if there are women willing to devote themselves to nothing but Healing sick or hurt people, it still requires them to isolate themselves hundreds or even thousands of miles, and thus weeks or months of travel by horse or second-rate boat (not being welcome on the fastest ships), from their society and sisterhood. The Tower works hard at taking the place of nation and family for their initiates, to the point where they really do seem to believe (based especially on their errant view of the Kin), that without the Tower, a former initiate would not even care much about channeling. They would not want to be that cut off from the Tower to that degree, especially to just sit around waiting for rather ordinary things to happen for them to help with. It's one thing to actively go out and about on her own agenda, but a whole other to be effectively exiled for such a mundane purpose.
I also don't see that there's much benefit to the Tower in providing such services. They have all the influence and respect they could wish for already. Giving stuff away for free and hanging around where people can get a look at them so easily only degrades their awe and mystery. The more you give people, the more they come to expect. They have no problem giving people stuff, they just don't ever want anyone to think the sisters owe regular people anything. Coiren negotiating with Sevanna is an example, where Katerine notes that she is setting up a loophole in the bargain so they can stiff the Shaido on their most important condition, even though they actually have no problem carrying it out, and even offer an affirmation (that by the First Oath must be true) that the request is fair. But they were still laying the groundwork to give their deal-partners the shaft if it was convenient. This is not the practice of a group that would give away anything they did not have to.
They can't deal with anyone in good faith, they set things up so they can bail or operate however is convenient for them, so why would they give out one thing more than they have to? Why give each city, each monarch, hostages to fortune, by always having personnel stationed in population centers? Why commit to a course that might lead to people thinking the Tower owes them something? We have medical capabilities that make yesterday's death sentences into minor inconveniences, and one of the biggest political battlegrounds in recent years was inspired by some people believing such miracles cost too much. On the CMB of this very site, someone posted an article brimming with outrage that a family was being charged a significant amount of money for emergency medical care in a remote location in a foreign country, that saved the life of a pregnant woman and her child. While going on and on about the extraordinary expense, no one stops to think that in effect, they are putting a price tag on the life of a baby, saying that a live and healthy baby is worth much less than a million dollars. Anyone who would sell their baby for a million dollars would be viewed as a scumbag, but people who refuse to pay that price to save their baby from nature's curse (or in that particular case, possibly their own ill-advised choice to fly while pregnant), who are in effect doing the same thing as the hypothetical baby-seller, valuing money over a child's life, have a sense of entitlement, that they are owed this wonderful service at a price of their choosing. Who, if made to think of it in those terms, would set a dollar amount on the life of their child? But that is what people are doing when refusing or complaining about the price of saving that life to be too high. But people have come to take medical care so much for granted, they no longer think about what they are getting, or how rare such a service or chance has been over the course of human history, how through most of that era, the most powerful kings would have been shit out of luck, though they might willingly have traded all their wealth or fortunes for a procedure that would actually save their child.
If that is the nature of humanity, how long before people stop being grateful for the miracle of Aes Sedai Healing for free to save their lives, and start wondering if Caemlyn can have a Healing place, why not Whitebridge, or Aringill. And if those towns can have permanent Healers, why not Four Kings, or Baerlon? If the Aes Sedai can Heal my broken leg, why not my bruised ribs? Then why not my sprained ankle? Then why not make a house call for my cold? The more they get, the more people want. There was a time when people looked at a Jurassic Park movie, where the first dinosaur you saw was flagrantly and obviously not in the scene with the actors staring in awe at it, when a lot of their interactions with the actors was slow and clunky and obviously not organic beings. But those special effects were better received and more appreciated than will be the case for the special effects of its third sequel coming out this summer. There are already articles and videos on the internet bitching about the quality of the special effects due to tiny, nit-picky details not satisfying the self-appointed connoisseurs among the viewers, based on a couple of trailers! An airplane flight can take you anywhere in the country in two or three hours, instead of months, with less risk of physical assault or privation, and yet, sneering at the quality and quantity of the food or snacks on offer for those couple of hours is so widespread as to become cliched. People can buy things all over the country without leaving the comfort of their homes, and mutter dire imprecations and obscenities about the possibility of a gift not arriving in time for Christmas, because they waited until December 19 to order it! This is human nature, and I think the Aes Sedai as a whole are shrewd enough to realize that's the road they start down once they start offering services for free like that. Elayne's all full of youthful idealism now, but just wait until she starts getting the grumbles and complaints, not necessarily because the Kin let someone die, or refused to open a gateway for a merchant who would not pay, but from people who had to wait three hours to get their cramps or backaches cured, from wealthy merchants or their wives or daughters irate at having to wait to get a cosmetic Healing, behind "some farmwife throwing up her litter". The gateway users will complain about the long lines to go through the gateways, or about extra fees for longer wagon trains that take longer to get through a gateway, or extra fees for an extra kinswoman to make a gateway big enough to accommodate an extra-wide wagon, or one stacked extra high. Or they will complain about the quality of complimentary wine served in the waiting area. No one appreciates miracles. I think that on some level, the Tower is shrewd enough to avoid getting into such a predicament.
“Tolerance is the virtue of the man without convictions.” GK Chesteron
Inde muagdhe Aes Sedai misain ye!
Deus Vult!
*MySmiley*