What has Egwene done that is against the wishes of her followers? Allow older women to enter the Tower? Raise Elayne and Nynaeve? Refuse a rescue from the Tower? Elayne has overridden her followers when she knew she was right, as had Egwene. For the rest, both have shown a remarkable ear for what people who follow them want.
And you're right, Egwene is an elected ruler, unlike Elayne. Which was my point... Egwene had to make speeches because she needs to bring independent women who don't like to follow orders to see things her way, to stop them from bickering, to make up for the deficiencies they've shown as an organization. Elayne doesn't face such issues, and hence had no reason o give political speeches.

When given by major protagonists in a fantasy novel? Yes.

No she did not. Sure, she wanted a powerful Tower to counter the Shadow, but the way she meant to achieve it was in direct contrast to Egwene's. Where Elaida banned an Ajah opposed to her, Egwene prevented the Reds from disintegrating and showed them favor. Where Elaida wanted to strip away each Rebel from their Ajahs and make them submit to her will for decades, Egwene has handed out no punishments at all, despite feeling strongly that Elaida's supporters had bungled.

Because she has a laudable goal for the Tower, and is not a megalomaniac like Elaida, and can hence actually achieve that goal?

Why the hell should she, or anyone else, be satisfied with merely being out of Rand's hair? What is wrong in wanting the glory of helping defeat the Dark One?
The Tower has worked to fight the Shadow for millenia. Just because it has done a woefully bad job of it in the past few years doesn't mean it shouldn't aspire to be back as a pain in the Dark One's butt.

Perrin has everything in hand in his camp. We have no clue about how his interaction with Elayne will go, so I'm only going to base my arguments on what Perrin worries will happen, and what Elayne has said she'd do.

How so? I don't for a moment think Andor is useless. I merely pointed out that by the reasoning you used to claim the Tower was useless, so was Andor.
I believe both will play central roles in the Last Battle.

No it is not. The Tower, as an organization, can unite the nations. Rand has them in a tenuous grip, but the Tower has the ability to smooth away his difficulties.
Further, Egwene's stated motivation to support the Rebellion is to keep Elaida out of Rand's hair, in which she has succeeded admirably. Elaida's wish to rescue the sisters Rand capured in Dumai's Wells, as well as her inability to send more sisters to help Toviene against the BT are a direct consequence of Egwene's actions which made the Rebels start moving towards Tar Valon.
Thus, Egwene directly kept the Tower out of Rand's hair, essentially fighting his fight against the Tower establishment for him.
Now that she has united the Tower, she has already ensured that the united resources of the Tower are not going to be used to impede Rand.

And which of these actions were desired by the Aes Sedai? They wanted her to help oust Rand. She refused, thus disproving your idea that she'd easily bend to Aes Sedai influence.

She said problems would be solved if he knelt to Egwene. Which is still a great deal more than Egwene has ever wished for or expcted! Frankly, it is a ridiculous idea, and Egwene seems to have not even conceived it. But Elayne trusts and believes in Egwene as Amyrlin enough that she hopes her boyfriend, the Dragon Reborn himself, will kneel to her. Which serves to prove my point that Elayne is going to be much more strongly aligned with and influenced by the Tower.
Sure, she won't do anything that is bad for Andor (nor will Egwene ask her to), but at the same time, she's automatically going to want good stuff for the Tower too. Which is not something that can be said of all the Queens of Andor. None of them were Aes Sedai, and none of them had such a close personal relationship with the Amyrlin Seat.

What can she guide him in? How to lead without appearing to bludgeon. How to deal with the frustration of fractious followers. How not to let the weight of responsibility make you insensitive to your inner humanity. How to be in firm command of yourself so that you can take the worst sort of punishment and still not be broken by it.
In so many ways, her problems were akin to Rand's, only smaller in scale. Yet, she succeeded in tackling them better than Rand did.

I might note that Egwene has not taken the Tower's side over Rand either.
But Andor was never the Tower's protectorate. The one instance where Morghase allowed Andoran interests to be subsumed to the Tower's, Siuan and Elaida had to talk with her for ages, and for all we know, she only caved because of the enticing possibility of a stable neighbor. Elayne is going to be no different than Morhase in opposing the Tower when required, only more effective because she is protected by the Tower's own laws about not interfering with another sister's business.

And my point is that this is so obvious, there was no need for all the verbiage. Its like writing a detailed, pointless, and at many instances stupid analysis of Rand's actions against the Shadow till this book to conclude that Rand will need a new strategy to defeat the Dark One. DUH!

No I don't. I have a very normal definition of the phrase. You're the one who twists it to justify your rabid hatred of Egwene.

Micromanaging? Don't raise a straw-man to argue your point. Rand didn't have to micromanage anything. A few trips to check on Taim when suspicious activity is being reported is only sensible, and requires no more than a few hours.
Egwene, of all the female protagonists, has shown the most sensible view of the Asha'man, even before she knew saidin was cleansed. She thought it foolish to try and destroy it before the Last Battle, she sent Logain to Rand, and she actually tried to help Rand learn to channel!

What the hell is the point of this rant? Where the hell did you get an idea that I think Logain is a good man and deserves power?
Really, cool down and read what I wrote! The guy may be the world's worst douche bag, but that doesn't change the fact that he has a significant following among the Asha'man. Rand needs to work with him to remove Taim, and that is inescapable fact.

So, two totally unrelated events are now mentioned in the same sentence? That is absurd!
Elaida was very wrong in her thinking that the fifty sisters she sent would be the cause of the blood and fire in the Black Tower. But the clear implication of her foretelling is that Aes Sedai will be involved in the event.
Now, as things stand, six Red sisters are likely trapped there, and that by itself will be reason enough for Egwene to start looking at the Black Tower. Add to that that 47 Rebel Aes Sedai are also likely trapped in the BT, and a WT-BT confrontation is almost assured.

Why wouldn't she use the considerable resources of her Tower to defeat an enemy? Your argument is irrational.