Can you imagine Romanda or some equally political Yellow agreeing to sit somewhere in the boonies Healing the occasional injury who wanders in? A large part of what makes the Tower work is that it doesn't actually order the sisters' lives. There is the hierarchy and politics inside the Tower, but you don't have to put up with that if you don't want to, and can go about doing whatever vocation inspired you to become an Aes Sedai in the first place. if they started conscripting and assigning sisters, the politics turns in a whole different direction and there goes the unity.

The Tower isn't an army, it's more like a combination political party and labor union. People are in it to further their personal interests, not the other way around.