> your chances of falling victim to random crime is basically zero, so they feel extremely safe in spite of having many crime rates comparable to places that feel extremely unsafe

Where are you thinking of? What I've seen, more commonly, is societies with lots of crime having ways for the wealthy to insulate themselves for it and then, acting against a background that has normalised high crime, feeling very safe. Versus societies where everyone is more mixed together where folks are constantly paranoid about vanishingly-infrequent crimes.