Let's see. They have the greatest library in the world. They were the ones who pulled civilization out of the chaos in the aftermath of the breaking, they were instrumental in the fighting during the trolloc wars and helped civilization recover afterwards. They were even the ones who tried diligently to keep "The Grand Coalition" together after the Aiel wars. And it was Aes Sedai who:
Kept the Dragon Reborn out of the Shadows hands early on
Kept the Shadow from capturing the Eye of the World and ending time itself
Took out two Forsaken, and captured a third
Rediscovered Traveling for women
Forced Moggy to reveal how to skim
Rediscovered how to make Cuendillar(sp?)
Rediscovered how to make Terangreal
Discovered out how to Heal men from stilling and imperfectly heal women
Were instrumental in recovering the Bowl of Winds and helped the Seafolk use it to make the weather right again (yes I realize that it was seafolk knowledge that "operated" the bowl, but AS power helped, especially with the Angreal they found.)
Aes Sedai were critical protection when Saidin was Cleansed. And a critical part of the team that Cleansed it. (passive yes, but not less critical)
An Aes Sedai got Rand out of prison at Far Madding
An Aes Sedai was instrumental in ensuring that Lan will have an army to fight with when the trollocs come pouring out of the Blight.

NaCl(yeah, I guess you are right, the Aes Sedai are superfluous)H2O