I think the basic problem with Egwene as Amyrlin is that she's sorely misinformed about what leadership and power actually entail. This is understandable, as she lacks any real-world experience of it. She went from a tiny village where power and authority were largely unspoken understandings, to the glittering world of palaces and kings where vassals bowed and scraped and spoke humble words. She never realized that this is merely the public facade, and that those same kings were continually questioned, challenged and balked by their vassals in private. It's not authorial ignorance, either; Jordan had a keen understanding of politics, as we see repeatedly. Rand, Elayne and Fortuona all faced constant opposition and had to build and appease factions in order to rule.
But Egwene really does believe that being a leader means unconditional obedience.
The only demurral I would make is that Egwene demonstrated her own awareness of the need to challenge a leader and to keep a ruler from getting too arrogant, which was her excuse for her constant stream of ridicule and vituperation when she was in his company. She has no idea how to offer constructive criticism, and even manages to not learn anything from witnessing her friends' much more effective styles of personal criticism. Elayne or Aviendha or Moiraine offer alternatives, they offer reasons, they demand reciprocity, and Egwene can only think to berate or refuse to engage. Moiraine even explicitly tells Egwnene what Rand will need from her after Moiraine is gone, none of which makes an impression on her by her subsequent treatment of him.
From that perspective demanding oaths of fealty is almost natural. Far from being a horrifying imposition that's the next thing to Compulsion when paired with the First Oath, it's becomes a sad but necessary step. A restoration of the natural order. After all, if they'd only obeyed in the first place, as they ought, she wouldn't have had to insist on it!
However it might worth asking: was Egwene necessary? Were the Aes Sedai so blindly factional and hopelessly broken that only a dictator could weld them together in time for the Last Battle? I'm inclined to say yes, especially with the Black Ajah working to widen the divisions. A sad indictment of the White Tower, and a sign that they've long since ceased to be fit for purpose.
I think a more precise way of phrasing this, is that only someone with Egwene's thirst for power and my-way-or-else mentality would bother trying to become that dictator. The established practice for the more sensible sisters seems to be to hit the road and get on with serving the purposes for which they became sisters and chose their Ajahs. Good Greys go out and negotiate or advocate. Good Blues go out and serve their causes (bad ones of both Ajahs stay home and get into politics). Good Yellows look for things to Heal, good browns seek out knowledge, good Greens look for things to fight and good Reds hunt male channelers before they become international threats. The people not inclined to change or challenge the system stay in the Tower and help perpetuate it, either by voting in Sitters and Ajah Heads with similar attitudes, or by serving those offices themselves. No good sister, genuinely concerned about the Tower's well-being AND that it refrain from oppressing or unjustly interfering in the world, would do what Egwene has done to take power. Justifications of a dictatorship automatically preclude the notion that other people's opinions might have some value.
“Tolerance is the virtue of the man without convictions.” GK Chesteron
Inde muagdhe Aes Sedai misain ye!
Deus Vult!
*MySmiley*