Can you, or should you trust a powerful organization answerable to no one but itself? Can an organization like that do more than incidential good for outsiders, more than what its members can do individually without the organization?

As has been pointed out, the only good were done by individual Sisters, without the need of a White Tower.

It is telling that the purposes each Ajah has are just mostly empty promises, escepially the Green, and the Yellow. For the Red, does it need to be the biggest Ajah to do its job?

So you kind of get it when you start to question their existance. The AS are written not as an example of ideals, but as something we should avoid. Of course the AS fail very hard, they are what you don't want to be.

Kingdoms and Empires are answerable only to itself, the rulers. And we no longer organize a country that way. We found better ways to do so. There are better ways to organize channelers than making them the current Aes Sedai.