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.

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