Who said Andor was critical? Significant, yes, as the largest group left not under the control of him or the Seanchan, but who ever said it was crucially important for him? Does Elayne give a Hitler-esque rant to her followers about the glories ahead and how she will whip them into shape and people with remember them in awe, when she takes control of a reunited country? Of course not. The point about the Tower has been that everyone has been talking about it as a crucial and important thing, that the reunification was necessary for the world and the coming events.

Tam's hint of what is to come in the next book argues otherwise.

Her survival is important, presumably because of some personal involvement with Rand yet to come, and for Andor's own good, but that is my point. It is the same with the Tower. The reunification of the Tower and Andor are both strictly internal issues that benefit on the organization and nation involved, and have little in the way of implications for the Last Battle.

What could she possibly have done, aside from cut into his time with Min? He's done well enough without her political advice, her channeling is to Rands as the White Tower's resources are to Rand's - negligible, and there is really not a lot that she could have helped with. So why not have her go off and do her thing. As for the wasting books, the Andoran story at least as a direct effect on Rand early on, as it provides motivation and psychological issues and so on. Elayne's own fight was a mere portion of three books.

She is going to be much better, what with Dyelin knuckling under so easily to Aes Sedai (on that scale, we can say that Elayne's victory makes that of the Tower even more irrelevant - a Tower-influenced ruler would be a reason why the Tower's support for Rand was needed. Elayne on the other hand, can only be turned against Rand by his own actions, and certainly not the Tower), and her stick-in-the-mud adherence to Andor's traditions and customs.

She is no better than the obstructionists who are the last to stand for Elayne, except she does not want the burden of rulership. That bunch is arguably just as bad as Rahvin's courtiers who backed Arymilla's claim, IMO, since at least Rahvin's group were honestly self-interested, whereas Dyelin's group was demanding to adhere to their special privileges even in the face of Tarmon Gaidon, while dressing it up in noble-sounding terms. Just like the Tairen & Cairhienin rebels, they wanted things their way, they wanted to retain their special privileges of rank, and the man needed to save the world be damned. At least the "bad" third could have been bought. Elayne's victory is better than Dyelin, because it marginalizes them, whereas they would have been the most influential faction in Andor under Dyelin (and for that matter, Morgase). Now Elayne's closest supporters, the ones who came to her when times were bleak, and who can claim the most influence for their support, are weak teenagers without long-standing issues and vested interests. The entire power structure of the country is broken and whipped into a shape that will work better for Rand.
This is a similar end that Egwene was seeking in her inconsistent and contradictory speeches to the Hall and the rebels - knock down and power blocs who might claim too much influence over her administration. She wanted firm control over the Tower, unencumbered by the pre-Dragon Reborn factional currents and old rivalries and agendas. And this might be good, too, presuming Egwene uses that control to do something positive, instead of squabbling with Rand to preserve Aes Sedai privileges and special status. We know Elayne will be on Rand's side. We cannot say the same about Egwene for sure.
So, as you yourself seemed to have realized in between all your muddled arguments, there is no point discussing this till we see where Elayne and Egwene take their respective lands.
And we know, as clearly as we do with Elayne, that Egwene will be on Rand's side. Sure, she may flay him for ignoring the Black Tower and letting his underlings do stupid things, but that can only be to the good. That will satisfy Logain and his huge faction of good Asha'man, it will lead to the removal of Taim and the exposure of the DF Asha'man, etc. Given that Aes Sedai are seemingly supposed to help in destroying the Black Tower of Taim according to Elaida's prophesy, Egwene may in fact end up being the pivotal to exposing and excising the traitors in Rand's organization. Proving again that the White Tower's reunification was necessary.

No one compares Egwene to Rand thinking the Tower is equal to the world. They do so because there are obvious character parallels, because their stories were shown to be connected, and because beyond any doubt, they are the chief male and female protagonist of the series. It is a matter of thematic similarity, not a similarity of scale.