I believe Egwene is also a Ta'Veren. Mat and Perin are very close to Rand, the Dragon Reborn, are Ta'Veren, why not Egwene, she is also very close to Rand. Look at all the events where people and event just seems bends to her as well. Wise Ones whom have distrust and dislike Aes Sedai , yet they willing to teach her dreamwalking; A barely twenty something Accepted got raised to be Armyrlin Seat; Aes Sedai hundred of years older than her sworn fealty to her. I don't think all the events that lead her to be Armyrlin Seat (being raised Armyrlin none of her doing), just as Perin became the Wolf Lord, and Mat's Band of the Hand and Prince of the Raven to converge for The Last Battle is all just by chance. Not to diminished her accomplishments, the 3 boys, they too had their challenges and they all had things gone in their favors. It is the Aes Sedai that declares who is Ta'Veren and I think they overlooked Egwene her because she is one of their own. So my theory is Egwene is the Overlooked Ta'Veren of the series.