Seems to me like mercenaries in a war zone and civilian police either public or private is a very different job description.
Personally, I rather like the structure of modern police departments. There is a good command chain of accountability. A department is accountable to the city council, AG's office, mayor and police and fire board. The people can remedy unlawful actions by the police with law suits, complaints to the department and various other entities, and by asking the mayor to fire the chief. If a mayor is in a corrupt chief's pocket, a campaign to unseat the mayor can be launched, attempting to replace him or her with a mayor who clean up the department. Even though flawed, this system is very workable for the greater good by those who take the time to use the system.
PD's already run themselves too much like a closed door private business instead of what they are, organizations of servants hired by and for the people. Any further steps to privatize the criminal justice system are in my opinion dangerous.
Though I will say I agree, mercenaries, and for that matter all types of legal private security forces are a good idea.