There are many dangers with allowing the state a monopoly on the use of force (even at the local level). If a policeman unjustly harms a civilian or commits an unethical act, the likely scenario is that the story is buried by the department. If somehow it makes it to the light of day, that policeman is placed on “administrative leave” (while usually still drawing a paycheck) while the tax-sponsored police department conducts an investigation. The taxpayers pay for the investigation in addition to the attorney fees for the policeman that perpetrated the act (I hesitate to call it a crime because crimes are only committed by the private sector, no?) If somehow the criminal policeman is found culpable, the court will award damages to the victim, and guess who picks up that tab as well? The taxpayers, of course.
But if there were private companies competing for the "business" of the use of force, the situation plays out a lot different and allows for the "rascals to be thrown out" at their own expense. See: Blackwater.
Another real-life example of the competition for the right to use force: