There are enough people of yondan+ rank with multiple dojos and students of nidan or higher, that I suspect we could have hundreds of new aikido orgnizations directly under hombu spring up if they all decided to do so.
Rob, this might have crossed my mind quickly and long ago, but I'm really glad you brought this up. I believe that having some diversity among schools, with mild or perhaps even moderate differing perspectives on the same art seems healthy. However, if more and more yondan or higher, to use the rank I think you chose well, were to become "shihan" of "hundreds of new aikido organizations," my brain and its taste for considering extreme metaphors thought immediately of the U.S. Civil War.
The majority, or at least the majority of the "people who mattered" in South Carolina wanted to secede from the union. Knowing the paramount importance of a "United" States, especially since one secession might set a precedent for other states, President Lincoln chose to go to war to preserve the union. This was far from a modern war; it was a war of close combat with bayonets to the solar plexus, with piles of people just alive enough to feel every agony until they died of bleeding, thirst or starvation on the battlefield. After a war with more American deaths than the tolls of every other American-involved war combined - to the point at which even many Northerners with all four limbs might have found their victory Pyrrhic, the states became united again.
I find a metaphor here. I suppose I could have just quoted Pink Floyd's "Hey You" and say, "Together we stand, divided we fall." At any rate, I think it's just fine to have a small number of schools. However, I think from where we are now, even a few more would be degenerative.