There is less to the idea than meets the eye, do not forget the counties:
This paper finds that disbanding police departments leads to fewer police-related deaths, fewer reported crimes, and lower law enforcement expenditures. However, the number of crimes reported by the sheriff for the entire county increases by an amount commensurate to the decrease in the number of crimes reported by cities that disbanded their police department. Furthermore, disbanding police departments is associated with an increase in county sheriffs spending which offsets the city savings. Thus, disbanding police departments does not appear to impact overall crime, shifts responsibility for law enforcement onto other governments, and reduces the available information about cities’ crimes.