The UK tried the experiment and gave up: https://en.wikipedia.org/wiki/Police_and_crime_commissioner

They were quite overpaid compared to other local government roles, and had very poor public visibility. WP says they were originally going to be called "sheriffs" but that was rejected as "too American". This does make it clear that it was an attempt to copy the US system, but I feel obliged to point out that the Scottish court system has had Sheriffs for longer than the US has existed.