They're an excuse not to render a service. If you're in need of protection from a violent neighbor or relative, the police exist as a thing we can say exist to solve the problem without actually solving the problem. If the police don't respond or treat your case with urgency, we're allowed to say that the urgency doesn't exist.

In a similar vein, they exist to exaggerate the threat of certain areas or populations. If you're constantly putting squad cars and doing arrests and send in SWAT teams through a neighborhood, we can say that the neighborhood must be very dangerous. More and more police activity in an area flag it as "in need of additional policing" because what would the police be doing except restoring law and order to a neighborhood plagued by anarchy?

They are, in effect, a tool of state propaganda. Their physical presence (or absence) signals what is taboo (or tacitly encouraged) by the city/state/national leadership.