What the media dubbed the Power Conferences, the NCAA correctly recognizes them as the Autonomous Conferences.
Those conferences were granted autonomy when the majority of Division 1 conferences voted to grant them that authority. IIRC, only 17 of the 351 members expressed opposition.
I suppose the AAC could seek autonomy, but I foresee the majority of the existing autonomous schools voicing their opposition. The NCAA Council would then not even vote on the matter.