Currently, the only way to restrict which users can post anonymously is by trust level. Would it be possible to add group membership as a criterion? So, for example, I could create a group “Alcoholics Anonymous” and anyone who is a member in this group can post anonymously, but not the other users.
At the moment this feature does not exist. Its possible to make such a change, @codinghorror’s call of if he wants it in core or not. Regardless I don’t think we will build it, would have to come from community.