He has he Aiel without Aviendha. You could make a better case that the Aiel brought him Aviendha. He isn't into her to make the Aiel follow him, the Aiel all but stripped her naked and tossed her into his bed. Though she has had good intentions in that regard, I completely fail to see how Elayne has actually done anything to bring him the AS. In any event, the Amyrlin Seat would be better suited for that, if she was so inclined, and Egwene would be in a better position to do so than Elayne, since placing a love interest above the Tower would be a grave misstep in Tower politics, whereas Egwene, if she ever gets around to promoting Rand's agenda, can claim that she is putting the greater good above everything, and even make herself seem admirable for placing her beloved Tower below the world's interests.

The latter, at least, is all-important to sidious.

Agreed. You can't even argue that the world or culture is unsuited to produce superwoman. Really, it is more difficult to make a superior man from this female-dominated society.