Interesting. I see what you mean. When I say do not move, I am sure you will understand, it does not mean I become entirely rigid like a stone statue. Perhaps displacement of the body in relation to the ground... basically reduce the number of actual footsteps....
I see many Aikidoka's first move their body and then (try to) unbalance aite. Again with move I mean footsteps.
I really like your take on "body fighting its own action". This has our attention in practise. Example: Why do you step back when you push? Uhm, I do know. Then stop doing that! Happens quite frequently.
The "when you push, why do you step back?" problem, how do you solve that? I never found the machinery to solve that within my aikido training, or maybe it was there, it was just never pointed out how the tools could be intended to solve it. Especially the fixation of the upright, rigid spine, and how it impacts the arms, this I am still working out of my body after years of training it in in aikido practice. And on the other hand, the answer to that question does not have to be a question of the body resisting its action, but of neglecting it in most places...