I think the main problem is that most halfway decent people pick a different occupation that police officer. I mean, if you're really into making a difference and helping your community, you probably run a food bank, or become a firefighter. If you're into whipping out your gun and yelling at people to, 'get on the ground', then you become a cop.
Lets be honest though, crime in this country happens every minute of the day. People are murdered, tons and tons of people are addicted to drugs, they rob and shoot people all the time. In the worst areas of our country, the police are little more than a rival gang among the chaos. But, what if we didn't have police? What would happen? I submit that, crime would eventually go down.
My first thought was that, shit would be completely out of control without law enforcement pistol whipping some mother fuckers every once in awhile to keep us in line. And that makes sense. But, most people don't break the law because they prefer order to chaos, not out of fear of the police. Conversely, most people that break the law do so for their own self interest, and while im sure they hope they won't get caught, it's obviously not much of a deterrent to crime.
So if you try to imagine a world without police, you think, well fuck why pay for my groceries, fuck this I'll just take em... So you walk out of Safeway with your shit until you get to the exit and the store owner shoots you in the leg and takes his shit back. This is the main point that I'm trying to make, the natural consequences of commiting crimes (ie someone killing you for breaking into their house) are replaced by law enforcement. So you're actually better off being a criminal when there are police to protect you than not. Think about the crime of rape, if it was up to the public, we would fuck people up in the worst ways we could think up every time a rape occured, until there were no more rapes. Or if some asshole beat up his wife all the time? he'd be dead too. It sounds brutal, but people that can't control themselves serve no purpose to society anyway, there's no practical reason for their existence.
I'm not saying this would magically work, and turn us all into a utopian dreamland, what I am saying is that eventually the people that pose serious risk to others around them would be weeded out, whereas in our current society they endlessly breed more future criminals, and we pay billions of dollars every year to pack more and more of them into jail. I mean its not pretty either way, but human nature is human nature, we worked together in harmony long before there were police telling us to do so.