I may be over simplifying this answer but I there are several reasons: First, for this or any other idea, someone needs to start the process - someone who strongly believes in what they want to form, who can bring others along in their thoughts, who can find good people to take on the roles (for free) and who have the knowledge to create the structure.
This lead person, if they want to be successful will need tons of actual, honest research to be sure of what has to be different or compelling in order to get people to join.
Later this group will need tons of āmarketingā introduce people and get them to join.
Then you need staff and org structure to run such a venture on an ongoing basis - to develop the programs that allow you to be a non-profit, to deliver those to the members in a cost effective manner, etc.
I think most AAās probably dont have the time or the interest in being on a start up team. They have jobs, or businesses, they have families, they want to have time to ride, they might volunteer at other things in their communities.
Its just plain hard. Its hard enough to put together a new (local) GMO and make it successful even though there is an existing process and template to follow. The concept of expanding something like a new dressage org to 50 states hurts my brain.