Wow, a ruler who's trying to expand her influence and territories? Truly groundbreaking.

Why should Egwene sit in the White Tower like a lame duck? Cairhien has been a place of squabbling nobles since the beginning of the series, and probably since the Aiel War. If the White Tower can gain the city, then why shouldn't they? It's obvious that Egwene wants to use diplomatic and subtle means to get the city (despite warmongering theories that have zero evidence to back them up).

This isn't even a new idea, though obviously because Egwene is involved from some distance its caused hysteria. Almost as soon as Moiraine was raised to the shawl they were pimping her to take over Cairhien using her blood line, and they definitely did the same with Elayne, and openly said so. Siuan, Elaida and Morgase wanted Elayne to be the first open Aes Sedai on the throne of Andor, and obviously Elayne answers to the Amyrlin above all people. So Andor is pretty much the White Tower's. Considering Cairhien is a city waiting to be taken, how negligent would Egwene be not to look in its direction?