I think if you just ask the question "should this task be done by a person with a loaded gun" about everything done by the police and put the "no"s in one pile and "yes"s in another you can start getting a good idea of the scope of the problem.

The goal should be to get to a process where the person with the loaded gun is not doing tasks in the "no" pile.

I don't care if the person doing those tasks is called a police officer or not as long as they don't have guns.