When I was growing up in the UK, my understanding was that a police officer is allowed to shoot someone if that person is shooting at them and their own life is in danger. Nothing less.

Where did this character of the terrified police officer come from, who shoots first and asks questions later?

Also, I would think police depts would be at the forefront of campaigning for gun control, but that doesn't seem to be the case. A police officer in the UK, for example, can safely assume that most citizens are not carrying a gun, but in the US it seems that the assumption is that everyone is armed, thus creating a scenario of jumpy and trigger-happy cops who shoot and kill innocent people because they are scared of being shot.