At the time she was raised, the world was going to the Blight in a bucket. Nynaeve & Elayne knew about the Bowl of the Winds and did not believe (with justification) that the Aes Sedai were taking it seriously. The world was in massive danger and they were the only ones interested or able to solve the drought problem. Fussing over White Tower technicalities and Aes Sedai BovFec is the kind of stuff Egwene does. Nynaeve and Elayne simply seized on the first opportunity to get away from the huge waste of their time Salidar had become, and went off to save the world.

If it made political problems for Egwene, that is simply tough noogies. The Amyrlin Seat and the Hall and the White Tower organization all exist to enable channelers to do their thing and provide solutions to supernatural problems. Yet Amyrlins and Sitters and all too many sisters seem to believe in the inverse: that channelers exist to reinforce the White Tower and bring it glory and power. That is probably related to why Nynaeve and Elayne were allowed to head off to Ebou Dar with so little protest - they were wild cards and too accomplished, powerful and new to the Tower (and thus not as thoroughly indoctrinated as longer-service initiates) to be quelled into being lackies like Theodrin and Faolain were. The powers that be in Salidar were happy to see them gone so they did not have to wrap their minds around the implications of these unorthodox "sisters." The idea that they might actually take action on their own seems to be beyond the grasp of Romanda et al. From their point of view, only "real" sisters have the capability to get things done, and the Tower and Hall are the axis of the world. The idea that a couple of girls with no real authority in the Tower could...matter...was beyond them.

From my point of view, the damage Egwene did to the Tower and its traditions and rules was a wonderful thing and needed to be exacerbated, not repaired. But even if it was not a good thing, and its repair was for the greater good, it still does not change the fact that the Tower had no right to take that axe to the status and rights of a sister just to recover the Amyrlin & Tower's fumbled authority.