I'm surprised you can see only two possible ways to explain Egwene's statement. Either she's power mad or she thinks Aes Sedai are light made flesh? Really?

What you're ignoring is a massive difference in perspective you as an outsider have of the Tower, and how Egwene perceives it. Sure, it has bungled. But you focus on those, ignoring the other side of the coin. What of providing the stability and strength needed to restart civilization after the Breaking? What of the foundation of the Covenant of Ten Nations? The wrapping up of the Trolloc Wars? Providing stability after the chaos caused by Hawkwing's death. The three thousand years of keeping mad male channelers and False Dragons at bay? The prevention of countless wars, the restriction of One Power use so that people are never forced to face it in war? Are all these totally meaningless? Are they supposed to be to someone who lives in a world that exists due to these actions?

Yes, the Tower as it is today is a poor shadow, both of what it can potentially be, and what it actually used to be. It is neither absurd nor alarmingly weird, though, that someone wishes for its return to its prior glory.

You're assuming Egwene wants a return to a Tower not different from the days of Siuan. But her actions have already shown that such is not the case!

You complain about the Tower not accepting all women. But Egwene addressed that!

You may complain that the Tower holds strength in the Power too dear, but Egwene shows no respect for that view, as she proved again by giving responsibility to skilled and mature novices, rather than the most powerful ones.

You speak of the Tower preventing other organizations from existing. But Egwene entered her job already resolved to never force the Wise Ones (as if they can be), and swore to Elayne that the Sea Folk would not be forced to join either. How you think she wants a unified Tower so she can dominate these organizations is beyond me. Wasn't that proof enough that you are blindsided about this character?

As for two Towers, and kings having their own channelers... sounds great, but how exactly is this different from pre-Luthair Seanchan? What is checking the channlers rise to power? How quickly will channelers become the powers behind most thrones, or actual rulers themselves, displacing rightful kings and queens?

What is to prevent the use of the One Power in battle, the use of Compulsion to force others to the channelers will? Sure, women have done these things even with the Tower around, but we have seen this at the times of the Towers weakness. A failure in execution does not mean the principle itself is flawed!

Why can it not be that Egwene wants a united Tower so that she can change it? Change it so it becomes the force it has claimed to be? So that it actually serves its purpose in the Last Battle? Whether you think she can do it or not, it is a noble aim, and she seems to have had enough success at it, for now.