I ran this past my uncle, a retired cop. His response was slightly different. He was trained to shoot only at a target he could hit, a concept similar to the “fire discipline” he learned in the Marine Corps in WWII. You might be able to hit someone square in the chest, but hitting someone in the arm is dramatically more difficult with any kind of gun, no matter what you saw Hopalong Cassidy, Roy Rogers or Nemo do. You don’t want a bullet wandering off and wacking Grandma, or wasting one of your six shots (he had a revolver when he was active) when the perp has a TEC9 with a couple of magazines.
Beyond that he said the rule was you never draw your weapon unless you think you will have to use it, and if you do use it, you shoot to kill - period. If you reached that point, you don’t give the bastard a second chance to get you or whoever they are threatening. The chest area abdomen are the most effective for hitting and killing, so that’s where you aim.