She was the youngest daughter of her family. She grew up with her parents at their most permissive and least strict, but with three older peers in her household, who had even greater freedom, greater privileges and greater societal respect, who had power over her. Also she was a short girl, in a family of all girls. Compare that to Perrin having to learn at an early age to watch his strength and be careful not hurt people (it is also probably not a coincidence that he is the eldest child in his family, and would have had responsibilities concerning his siblings, in addition to being strongly enjoined against harming them even by accident, as well as being under more stringent supervision growing up). Egwene was never taught limits of her power. Since the people she butted heads with growing up were all more powerful than she, she learned to both resent their advantages and to push as hard as she could without needing to restrain herself, since her sisters or parents could restrain her if needed. Adora, Deselle, Paet, Bode or Eldrin had no such recourse against Mat or Perrin, so they would have learned harsher lessons about the responsibility that comes with agency.

Another thing, is that people are fond of calling her "the Innkeeper's daughter" as if that indicates some amazing rise in spite of a lowly origin. Nobody goes around praising Mat or Perrin, the Farmer's Sons, or Rand as the Shepherd's Son. At least those titles are complete. Because Egwene is also the Mayor's Daughter. Oh. Not so much of a humble origin now, is it? Also, innkeeper is a rather archaic term nowadays, so it sounds more lowly than it actually would be in the Two Rivers, where the al'Veres would have been one of the more financially prosperous families.

Egwene didn't need a taste of power, when she grew up in relative privilege.