In Los Angeles, crime on the Metro public transportation system has fallen by almost 70% in the three months since the LAPD was booted off the job and replaced by...security guards.

This is pretty good evidence that high crime rates in cities with large police forces are directly related to the police force not actually doing the job it's already being paid to do.

(LA Metro was forced to use LAPD for security a few decades ago, at which point crime rates went from very low to skyrocketing. LAPD serviced the Metro contract exclusively with officers that were in overtime hours (1.5x pay) so at best could only provide 2/3rd of the contracted manpower. That changed earlier this year; the contract was terminated for cause and LAPD was replaced with contract security guards. The contract security guards make substantially less than LAPD officers, so Metro is currently able to field a security presence about 5x the size as the LAPD force. Metro reported this that crime has fallen dramatically in just 2 months.)