I would bet most shots at the police aren't because the criminal wants to straight up murder a police officer out of anger in the heat of the moment. Rather because he's scared, wants to flee, and his only option left for that is his gun.
It's a given here in the US that the moment you as much as appear to draw a gun at a cop, you're getting shot. So I don't think criminals even have to think about it to know that it's a "kill first or die" situation, once you're down that route. Now, if the criminal knows that the cop is unarmed, all of that changes: his gun is just leverage. He flees (or expels the cops off his house), which is undesirable; but then's when the situation can be escalated. No more "wild West" situations of "this guy might shoot me any moment, better be prepared to kill him for my life".