I think you have a point. The Aikikai is the parent organization of Aikido and represents the last developments in the art of Aikido as taught by the Ueshiba family. The others are not only reflections of what the Founder taught at different times but they are also representations of what those individual leaders discovered and developed themselves.
O Sensei said that Aikido had no set form - that it was a "study of the spirit." My own teacher has said to me that Aikido has no form. If that is the case, then the styles are not what this is about. That's why many styles are allowed within the Aikikai.
Aikido is about principles and when those universal principles are in play, you have Aikido, whatever the style.
Aikido organizations are not really about styles. Like all organizations, they may have a product to promote and indeed, one that distinguishes them from other groups, but they are really about jurisdiction and authority. The battle of organizations is one to gain power through greater jurisdiction. The great names the organizations promote are to establish authority thus helping them in the quest for organizational "life" or jurisdiction. That is not to say that all are equal or as efficient and fair as they could be. That is a matter of organizational integrity and ethics but when push comes to shove, the organizations are about jurisdiction and establishing authority by means of gaining legitimacy and respect in the eyes of the public. (Size and an early point of origin are helps in the quest for legitimacy.) As that (legitimacy in the eyes of potential and actual constituents ) rises and falls, so does the fate of an organization. The Aikikai certainly has an advantage there but all the other organizations have to play the same game because they are playing in the same arena.
It has been my dream to see Aikido being united all over the world (Creating situations where any Aikidoka can cross-train at any Aikido dojo anywhere in the world without feeling guilty of "betraying" one club over another, or without feeling the pressure of choosing only one club over another).
It seems that this will never be practically possible.