This is definitely not correct. You are saying the police are safer if their strategy is "shoot immediately". If that is the case, they've just eliminated any i

This is definitely not correct. You are saying the police are safer if their strategy is "shoot immediately". If that is the case, they've just eliminated any incentive for someone with a gun to not shoot at them or to resist arrest. In many cases, the cops do not have the advantage, and if you know with certainty that you will die if the police get the first shot, you will shoot at the police at the first opportunity. You don't open the door and talk to the police. You find a place where you'll be protected and wait for the police to walk into the room. I don't know the exact probabilities of each of these events, and it would depend on the situation, but it's dangerous to assume that the police are better off if they open fire just to be sure they kill the bad guy.