I think that the Game theory suggests that cops will be less inclined to show up to a call or do anything to fight crime, because it could bring too much legal responsibility. Eat donuts, ignore the radio and you will be fine.
Except that it’s their job to do so. It’s relatively trivial to check what a police officer is doing if the department cares. Doctors can be sued for malpractice yet they still perform operations.
If we increase (already high) risk of being a cop, then we will have to be ready to pay 200k-300k salaries.