The issue is that Aes Sedai are supposed to do what is best for the White Tower. Always. Sure there is the belief Aes Sedai have that whatever is good for the White Tower will then trickle down and be good for the rest of the world, but ultimately it is White Tower interests that they wish to preserve and enforce.

As far as we know, there have either been no rulers that were also Aes Sedai, or they were very, very, very few. So such a conflict of interests as Elayne represents has never occurred before. And her actions show that between her homeland and the Aes Sedai, she chooses the former. And, she has basically become the second most powerful Aes Sedai due to her actions. Any Amyrlin beside Egwene would be sweating when she found out about this, due to the huge threat it poses to her authority. With Egwene being the Amyrlin, and her and Elayne being friends, it just makes the situation even more muddled and confusing.

So basically... Either Elayne is still in the Aes Sedai organization, and has simply grabbed power for herself when she had the chance (maybe do some sort of penance as punishment, etc, and establishing a new and uneasy balance of power within the Tower), or she has become a "rogue" Aes Sedai. At least that is how the world would see this, and the other Aes Sedai.