I have grave doubts whether Cadsuane would find any interest in correcting Egwene because not only is Egwene less influential, her problem is exactly the opposite of Rand's!
Where Rand thinks everyone should do as he says just because he says it, Egwene is wary of imposing on women who have sworn oaths to her!
Where Rand wants an army that is eagerly looking for death in battle, and thinks only success at Tarmon Gaidon matters, Egwene thinks that every citizen, every Aes Sedai and every soldier is important, and is reluctant to shed any blood. She's stupid enough to put the life of a novice from her home town above her own, and is imprisoned because of it.
Where Rand bad mouths people sworn to him, Egwene is courteous, and only comes close to yelling when one of those women breaks her oath.
Whatever success she has achieved, whatever domination she has established, she has done so while maintaining a facade of calm control. Hence, even an abrasive underling like Romanda can find grudging respect for her actions.
As for Egwene's supposed tyranny over the Novices, we know that most of it is due to one single incidence where Egwene was doing what was legal and right, and the rest is just talk from the Accepted to keep the Novices in check. Her "tyranny" in no way demeans her in the eyes of the women whose support and respect she needs.
Egwene's problems are much easier to sort out, unlikely to cause the destruction of the world, and certainly not something that cannot be handled by a few stern conversations with Cadsuane.