Have you considered that there being “a lot of crime” might indicate that police aren’t very effective at reducing the crime?
Police do not prevent crimes. They don’t leap out and stop muggers, or knock men who grope you on the head. They also hardly ever solve crimes after they happen. They won’t even look for the person who robbed you. They may look for a murder— but they hardly even solve half of the cases. Fewer if the victim is poor.