Bear with me for a second, but the purpose of the police and justice system is not to prevent crime. These systems are actually there to prevent vigilante justice, which invariably leads to innocents being killed to appease the mob (a la witch trials).
By having law and order in place, the people who might take justice into their own hands are now instead pacified by the notion that those who commit crimes will receive their due punishment. Is the system perfect? Hell no. But it's far better than the alternative.
Something else I want to point out is that this system is clearly working. Right now, humanity as a whole is the least violent it has been in all of history. There is plenty of data to support that your chance of being killed by another human is dozens of times lower than it would have been hundreds of years ago. And this is not just in developed nations, but all across the world.
It's easy to feel like violence is increasing, but that's only because society is becoming more and more attuned to the immorality of hurting others. We are now much more cooperative as a species than we once were. This, ironically, means that even the lower level of violence we witness in the world now is enough to make us feel repulsed.
RE: A World Without Police Monopolies on Force & Violence