Mary Sues are super-capable characters just because the author says so. The "everyone likes her for no good reason" is usually only a Mary-Sue trait in works that focus on romance (i.e. Twilight). If Egwene were a Mary-Sue, she'd be capable and competant and would run circles around everyone else, while being a saint. Instead, reading between the lines of the books, her scummy character is clear to see, and when compared rationally to other characters, with some perspective, her accomplishments and abilities are distinctly inferior. She is the least accomplished of the three so-called "Wonder Girls" and her accomplishments have the most qualifications and shortcomings. For instance, their unique discoveries: Nynaeve's Healing of severing was a truly singular accomplishment, done all on her own and never done in the known history of channeling. Elayne's rediscovery of ter'angreal-making was not unique, but it was all her own. She studied ter'angreal and figured out how one of them worked and from there, extrapolated the principles in order to be able to do it herself. Egwene pissed and moaned about Rand being able to Travel while she could not, received advice from him on how he did it, and only attempted it when she had confirmation from Moghedian. Who gave Nynaeve or Elayne advice of that level in their efforts towards their discoveries? Elayne did what 3,000 years of Aes Sedai studying ter'angreal failed to do, and Nynaeve was actively discouraged from pursuing her discovery. Not only that, Nynaeve and Elayne put Travelling to far better uses than Egwene does - Elayne uses it to defend her city against vastly superior numbers and unweaves a gateway to keep the secret from Seanchan hands; Nynaeve uses it to possibly save the borderlands by placing Lan there to rally the Malkieri. Egwene uses it to exacerbate the strife in the White Tower, and get the siege of Tar Valon started in time to prevent Elaida being deposed, she handcuffs one of the greatest living generals from using it to bring a speedy end to the conflict, and Egwene's own ineptitude results in the Seanchan getting their hands on a Traveler anyway. Meanwhile, Nynaeve blows Egwene's accomplishments in T'A'R out of the water, despite the latter's natural talent and frequent criticism or ridicule of the former's ability.

All in all, these are not the typical workings of a Mary-Sue. If Egwene was made out to be clever enough to outdo Nynaeve in Healing, that would be a Mary-Sue trait. The obvious superiority of other characters to Egwene undermines her qualification for that role.