Igor - that's a great 'Emperor's New Clothes' question. The conventional wisdom, which I've accepted - and may be true - is that the term 'aikido' was selected as a catch all for any and all koryu grappling type arts (torite, jujutsu, kenpo, kogusoku, etc). The idea being that whatever name was chosen, those referred to by a different name (yawara as opposed to koshi-no-mawari, for example) would choose to be insulted.
Hirai sensei had experience with Takeuchi-ryu as well as a number of other arts, and was actually "During World War II, Hirai was the head of the jujutsu department of the Japanese Army's military police school and was instrumental in developing a new arrest technique employed by the military police." So, somehow, he was, even then regarded as far more than Ueshiba's student.
That is one of the things that puzzle me. Didn't all koryu arts also deal with weapons? Be it defense against weapons or having a weapon curriculum?.
By this link http://www.koryu.com/guide/takenouchi.html
, Takenouchi ryu also had various weapons curricula. The only koryu that i can think of that didn't have techniques with weapons was Kito ryu and even those throws were officially presumed to be done in full armor.
By the standards presented also by you in your book Dueling with O'Sensei AikiBudo was definitely not a koryu. I don't know what was Hirai doing at the time but if it was similar to what we know today as Korindo Aikido it was also most definitely not a koryu. Did they basically just try to take out all of the taijutsu techniques from various arts and group them under one singular term? Also would that mean that many arts of the time actually had some mentioning of a term similar to "Aiki" in them?
But it's a fair question if there was actually a 'category' of aikido that subsumed all these arts. I just did a cursory search in Japanese, and it was actually a little hard to find references that weren't related to sites associated with Hirai Minoru. I wonder if it was Hirai's own 'baby' within the Butokukai - and never really went anywhere in terms of organization or enrollment. Remember that Hirai, although the general manager of the Kobukan, claimed/regarded himself as a younger peer of Ueshiba, not a student, and that what he was doing was a form of parallel evolution. I wonder if, in fact, the only 'members' of the Aikido-bu were Ueshiba's aikibudo and Hirai's Kogado.
This would seem to be the only logical explanation.