Reading the thread above, I guess one part is not very much discussed : yes Egwene was an ambitious young woman when leaving the Two Rivers, and then encountered Moiraine which was an ideal Aes Sedai - which could have influenced her. At this time, she has no strong beliefs about the White Tower, she still is somewhat overwhelmed by the White Tower - maybe thinking all Aes Sedai are like Moiraine - and that she can help Rand from within.
Then she is tricked by Liandrin, and becomes a damane under the Seanchan at Falme - unlike Elayne and Nynaeve. She is tortured psychologically, and we know that even experienced Aes Sedai are broken under this kind of treatment. I think she was a damane for weeks or even months.
Now imagine the impact of such torture on a 18 years old. Her survival instincts say that she doesn't want to be collared anymore. What is the best, no, the only way to do so ? Only by having a strong White Tower to counter the Seanchan.
So yes, Egwene is seen as very driven about the White Tower, unlike the other protagonists. But she was also traumatized in ways that no other protagonists encounter - until Rand is forced in a box.