(For)Tuon(a) needed a bit of a push in order to prompt her to launch the raid on the White Tower, and the raid was essential in bringing Egwene to the Amyrlin Seat. Specifically, it was made clear earlier that Adelorna and the Greens didn't particularly like or accept Egwene; this changed after the raid.

Additionally, Tuon won my deepest respect in that scene as the only person to date to meet Rand's gaze - at a time when he was more or less a personification of the Shadow - and still resist. In many ways, she is the female equivalent; death is nothing for her compared to duty, and she is a very hard woman - though Mat may have started cracking that shell.