I don't deny your conclusion (much less the facts). But it's a scary job typically around a bunch of scary people (it's not Andy Griffith). Also there's the psychological factor that (people tend to believe that) you'll fall off the roof through your own error, which you'll be smart enough to make, while when you walk up to the stopped car the person could pull out a gun unrelated to what you do beyond walking up to talk. The stress comes from belief, not statistics.

I think the oppositional model and recent (last 30 years) glorification of militarism has caused grievous damage to the functioning of civil policing. Non of which excuses police abuse -- and in fact AFAICT encourages it.