A lot of places self insure, but some already buy insurance as you describe. Qualified immunity is a pretty high bar to get over, but some people do get settlements. I’d argue insurance should have to be bought by the officer, or their union to have any effect on their behavior.
Crash. In high school my buddy brought out all the weird horror and b-movies he could find, including crash, a movie about people who get busy after dangerous or injurious automobile incidents. Cut to a few years later, when my friend’s parents are telling me a how they thought crash was so powerful and everyone should see it, and how it was nominated for a bunch of oscars, I was completely perplexed.