His massive lack of interest in organizations at any level has been mentioned by many of the uchi-deshi.
That's why I'm saying that calling it "the Founder's organization" is probably less accurate than calling it "Kisshomaru's organization".
I think in the beginning neither Morihei Ueshiba nor Kisshomaru had much choice in the matter. The Kobukan was incorporated in 1940 and it would seem that the pressure to do so came from Ueshiba's backers like Fujita Kinya. Kisshomaru would hardly have been in a position to contribute much and so it would be inaccurate to call the Kobukai 'Kisshomaru's organization'. Seko Seiichi did most of the work at this time and I knew him quite well, for he was my predecessor in the IAF. He and Fujita certainly had very strong support from Morihei Ueshiba.
Kisshomaru seems to have been more closely involved in the decision to reactivate the Kobukai, and to change the name, in 1948, when his father was still keeping his head down in Iwama. The main supporters of the new Aikikai were Morihei Ueshiba's old wartime supporters like Tomita.