This is a great idea. If we could have a fighting chance, however small, of regaining control, it would make certain animations much less annoying. It's not just that these things happen randomly, which is fine since you need to simulate mistakes, but that you're not able to smash a button, release the stick, do something to at least stay engaged with the game during the animation.
You should still fail most of the time but feeling like you are fighting for control rather than being helpless would make formerly frustrating moments actually engaging.