Because people don't just break the law, or shoot people only in city limits? If Tulsa elected a (D) mayor tomorrow, I wouldn't say that the Democrats controlled the city, since the makeup of 3/4 of the state government would still be Republicans who control where the majority of the state's funds go and who control the laws regarding things influencing inner cities like Minimum Wage, Housing, Drugs, Guns, Abortion, Voting, Criminal Sentencing Etc...
The problem here isn't that police aren't (overall) doing their jobs (something I would blame on a mayor).... it's that there's a bigger cultural / societal problem that the state and federal governments aren't addressing.