Most of these young women we encounter in WOT seem to have some sort of brain damage. The female Aes Sedai more so. Nyn isnt as sophisticated as others, and she hasnt really been initiated into Aes Sedai games yet. And as has been said in the OP, she does seem to have a better heart, compared to the others we have seen. She seems to care for individuals, rather than seeing people as chess pieces on a board, which both Rand and Egwene did until now. Rand seems to have stopped that. Egwene and the female Aes Sedai havent.

When RJ said, break what is there to build anew, he also meant the Aes Sedai and the WT should get out of their fossilized way of looking at the world. Hope they lose those blinkers in time. And once Egwene realises that, the whole WT might too. Moiraine realised that, and that is one of the reason Rand respects her among all the other Aes Sedai he has encountered. Same for Nyn too.