Doesn't it seem that all or most of the important Aes Sedai contributions (like killing the Forsaken and such) have come from those that have left the Tower and the Clash of Titans?

Moiraine spent most of her life outside the Tower. We've never seen Cadsuane in the Tower. Etc.

It seems like there are two factions that are/were struggling for power within themselves (Tower and Rebel), while the third actually avoided them both and is actually helping the world. Even Nynaeve and Elayne can be seen as belonging to the "neutral" faction, despite their sympathies to Egwene. They did not waste their time trying to put Egwene on the Amyrlin's Seat.

I don't think AS have no capacity to help, just that the Tower and their ridiculous deference customs severely restrict that capacity.