Indeed. While off-duty and in my marked PD vehicle, I carry with high capacity in mind for the very reasons you have provided. When I'm traveling, like in NYC for instance, I carry off-duty with a non-LEO mindset and typically a .38 as capacity is not nearly that important. A S&W 642 with a speedstrip reload would feel very comfortable in any place I don't have to worry about being the police.Comparing police shootings to the broad concept of general carry is nearly meaningless. The distances, the motivation of the attacker, the reactive nature of the encounter, etc. are all different.
Citizens vs random violence win or lose by surprise, speed, and violence of attack.
Surprise: Firing from ambush (home invasion or 3rd party defense while the bad guy is focused on someone else or feigning compliance until bad guy is distracted, etc)
Speed: Some take speed to mean a hell for leather draw, which is typically not the case. Speed is once you start any action that signals you're starting to fight you start the timer for them to notice and react, so some speed is required, but no false starts, no presenting a non-functioning weapon, etc.
Violence of attack: No hesitation, no standing there waiting for them to grapple the gun, but a committed attack until the threat is out of the fight, either down or disabled or fleeing.
Police, and targeted attacks in general, always look different. Higher round counts, greater distances, less chance for surprise on the defenders' side, and a much more highly motivated to stay in the fight adversary. The bad guy who's mugging you wants to live to mug another day and fleeing in the face of resistance is a great way to do that. The bad guy shooting it out with the police knows he can't just run away without being chased. Or he's already decided he's willing to die. Same with the jilted ex- who doesn't carry if he dies as long as he gets you, too. Much much different scenario and combining all these types into one bundle labeled 'average shooting' creates data that's meaningless to any of them.