No, you'd have to waste it on personal protection instead. Those who couldn't afford it, would get murdered. A great way to fight poverty - Kill the poor.
Um, the government isn't giving me personal protection very well right now. There isn't any reason to believe that crime has anything to do with law enforcement. The most peaceful places (like say Switzerland), spend almost nothing on law enforcement (compared to other countries). And places like the U.S. or U.K. that have high amounts of crime, spend a boatload and have quite draconian "crime control" measures.
There is every reason to believe that if you had a extremly small, community based police force, that focused on fighting real crimes (murder, break-ins, rape, abduction), and didn't worry about victimless crimes (drugs, prostitution, not wearing your seatbelt or motorcycle helmet, playing violent video games, showing your tits in public, smoking in resterants, etc.), that crime would be a lot lower - and it would cost a fraction of what law enforcement does now.