I think the kind of danger police face is scarier though, and leads to more stress. Most people aren't very afraid of getting into a car or drinking soda, even though those are probably the two most lethal things any of us will ever do. It's not scary because the way in which they harm us is abstract and seems controllable.
When there is a shooting, on the other hand, everyone is terrified, and we spend days and weeks worrying about it amongst our friends and on the news. Because getting shot is very concrete, and totally out of our control.
And I think danger from human beings is in itself more scary than danger from inanimate objects. Maybe because we know that deep down if a human being is trying to hurt us they'll probably succeed. We know we really can't control another human being. We rely on social graces to keep us safe and when those are gone we are in a very scary place.
American police operate outside of those social graces all the time, and they never know when they'll depart them. It creates a lot of stress that "one day I may be pulled over the edge of the boat into the sea" doesn't.
Incidentally, this is a justification for de-arming first responder cops. It creates the assumption for all parties that the cop will stay inside social graces, keeping everyone safer, and de-stressing a situation.