Can you name a big city run by Republicans? The only one I can think of is Miami, which has one of the highest per capita murder rates of any major city. It literally has a murder rate three times higher than New York City.
Over the last 30 years, there has been a huge drop in big city crime, with a huge jump in rural crime. The left behind red counties have fallen into violence and drugs. Postmodern will claim they are not big cities, so do not count... But they are the big problem as far as murder today.