The Sea Folk channelers inhabit a highly specialized position due to their talents that is extremely beneficial to their society. So while they aren't exactly integrated into it, they do serve the common good, are accepted like regular, normal people, just with a special gift. Some people are good public speakers, some are good at fencing and sword fighting, but somehow none of these groups are obligated to take vows to prevent them from doing evil. Not doing evil is just the assumed behavior for everyone due to morality. Aes Sedai don't need the three oaths to survive. They do need the three oaths to survive if they continue to be manipulative, egocentric, secretive and selfish, as they have ever since the AoL. The oaths are a band aid preventing them from bleeding to death, but they're also preventing them from actually healing and becoming a better society too.

The Wise Ones make an even better case, because they truly are integrated into their society, and there are Wise Ones that are not channelers, and that are regarded as even higher than the channeling Wise Ones. This shows that even further they understand that being a channeler does not change one's humanity, it is simply another ability to use. If Wise Ones and Sea Folk can do it, then so can Aes Sedai. They reason they haven't is that they don't want to.

This way they have a defense mechanism that makes them the victims should anyone decide to not put up with their crap anymore, because they are helpless and can't attack anyone except in defense of their lives. So don't threaten them, and they won't be able to harm you (directly). And this is enough to give them a moral high ground and keep the world from overturning their organization. If their protection went away and they continued as they currently do, another Artur Hawkwing would rise up and this time civilization would not rest until they were exterminated or enslaved, as the Seanchan did with their channelers. So to avoid that fate, the Aes Sedai would have to change, and start living up to their name. Which isn't something they are interested in doing, and therefore they'll keep their Oaths, thank you very much.