I don't really get how you jump the other powers and go to the one individual whose lost authority and control over the course of the series.

The White Tower could fill that vacuum quite easily under Egwene, and the fact that Nynaeve and Elayne are poised to be Queens, with Mat possibly being an Empress's consort with much more power than any of them.

Basically, while I appreciate that you are a Min fan, I'd file this under the "No Way In Hell" subject. Heck, Min's running thing in the beginning of the series was that she didn't want to be answerable to anyone and a desire to be independent of authority. Even her relationship with Rand shows her mistrust of authority figures and leaders - frequently, knowing the future impedes his ability to make a decision because he isn't as mature as Siuan Sanche or an older character.