What would you say to practicing XYZ say a dozen more times versus pushups, or other PE class exercises in terms of corrective behavior?

Doing the pushups is always followed by repetition of the technique. The pushups themselves are negative reinforcement to ensure the mistake itself is not also repeated. I used to have a coach who always said "Practice make perfect imperfection." If you do not reinforce the mistake that was made it will be repeated and the more a mistake is practiced the harder it is to break out of it.

I'm sorry I'm not sure what you mean by "other PE class exercises"