Um, you could ask Ellis Amdur, but he might not be interested in repeating what he's already written
I have indeed read and enjoyed those articles, but they seemed to be more about the history of aikido and Daito-ryu; they don't seem to directly address, "What the heck is a kotegaeshi for?" As I said earlier, I seem to recall Ellis Amdur saying on other occasions that he felt the techniques of aikido themselves are mostly movement exercises and such, of the tai chi variety, mixed up with O-sensei's spiritual and metaphysical beliefs.
There is the one mention of functional origin:
Ellis Amdur wrote:
It is true that this, too, is congruent with the history of the general development of jujutsu - battlefield grappling, particularly kata trained on one’s knees or with a standing opponent against one kneeling, with the wearing of light armor imagined whenever practicing the kata, was morphed into jujutsu - self-defense tactics for unarmored individuals in peacetime or police actions. The desperate moves for survival when one prepared for trying to counter a stab with a dagger with empty hands - contingency moves for a worst case scenario - were flipped, so to speak, into the central methods of jujutsu systems. Hand-to-hand combat drill became self-defense.
If so, this is very unfortunate, in my book. These do not sound like great techniques to begin with ("desperate moves"), and they don't sound much like what few techniques have been devised in modern times for such desperate situations and found to be effective. It would be somewhat disappointing if aikido dojo everywhere were engaged in the dressed-up study of absurd old combatives-manual techniques.