I have fortunately never been in a gunfight. I have learned enough in the various activities in my life to know that you have to focus on the task at hand in order to be successful. If you get rattled and neglect proper technique then you are relying on blind luck rather than skill. I know for a fact that it takes longer to miss 3 times than it does to aim.
I tried to google it but was unsuccessful but I remember it was a famous New York detective that has survived and won over 20 gunfights. He said that the other guy almost always fired first. The secret to his success was that he kept his cool and took aim.
As far as how serious police take the various aspects of their jobs; I have an old friend who is a police officer. He is allowed 30 minutes a day to work out at the police gym if he chooses to use it, he does not. He is allowed to go to the range on "company time" and is supplied free ammunition to do so. He does not. Once a year they have 1 week of mandatory training, Pistol, shotgun and some fun assault weapons as well as baton and hand to hand.
To his credit, I knew him because he was my student when I was teaching karate.
I'm amazed that more LEO's don't take physical fitness and training more seriously. I know that some do but my guess is that 75% do as little as possible.