Cop showed up at my house 2 days ago at 2am. Roommate apparently sleep-dialed 911.

Obviously situationally dependent (where you live, why you're calling) and of course you should have the ability to defend yourself if the cops fail to preform, but all that aside, that is not a universal truth. I called my local PD # a few weeks back because someone on a scooter got hit by a car in front of my house and I called the police (local PD directly, not 911, 911 would have been slower) and they had a unit at my house in UNDER TWO MINUTES. It's literally four minutes to drive (sans lights and sirens) from the police station to my house.

I know my experience is anecdotal and not universal, but neither is the "cops won't show up" one.