reverse-voltage protection

[kamocat]

I was thinking about how to implement reverse-voltage protection on a Jaguar or Victor, and I realized that all the polarity sensitive components, with the exception of the electrolytic capacitor, are powered by the 5v or 3.3v regulators.
Couldn't we just put a diode on the supply side of both of those, and thus prevent the motor controller from turning on when voltage is reversed?
(The capacitor, though it would blow hot oil all over everything, can be replaced)

On a similar note, how is providing power to the wrong side different than normal operation? It's still the same to the h-bridge. Why does the motor controller even turn on, if the motor is stopped? The source and drain on a MOSFET can be flipped without issues, correct?