But she doesn't really do that. She adheres to no abstract principles or set rules and order. She pretty much adapts her point of view to what fits her circumstances. It was that way from EotW on, when she embraced the Tinker fatalism in order to enjoy herself among them, since there was no way to achieve any of her goals in the meantime. She never seeks power to achieve a particular end, the gaining of that power is her end, as she sacrifices many previously expressed intentions or goals in order to secure her control.

"She...May not deal in doubt or pity--must not swerve for fact or jest
These be purely male diversions, not in these her honor dwells...

She is wedded to convictions - in default of grosser ties;
Her contentions are her children, Heaven help him who denies!--
He will meet no suave discussion, but the instant white hot wild,
Wakened female of the species warring as for spouse and child."
Egwene is totally a stereotypical female.

Seriously though, the most memorable and noteworthy thing Egwene did in the Tower was stand in a hole in the side to defend against invaders. She was literally the mother defending her home and children. She never fought successfully in the masculine manner - her only combat achievements were self-sacrificing, healing and protective. Rand's greatest battle achievement was going into a hole to impose his will. You don't get any more archetypal masculine than that.
More like the virile patriarch. He doesn't do any nurturing or care-taking, he simply sets things in motion, and imposes his will and order as best he can. It is left to his mates to care for the world he saves, and to maintain what he got started.

Actually, pertaining to the use of that term in the series, Egwene is totally the eponymous character of the book. The Lord of Chaos is a figurehead, specifically chosen for his or her unsuitability to lead, whom all make a pretense of obeying and serving, in the full knowledge that his reign is coming to an end very shortly. That meaning would seem to be confirmed by Taim's use of the phrase when the Reds ask to bond Asha'man: he was warning them that even as the bondholders, they would have no more power than the lord of chaos of the festivals. Titling the book where Egwene is raised as Amyrlin "Lord of Chaos" can mean nothing else.
He never had that revelation, his insight was regarding the Dark One's impotence.