Economics tells us that when there is competition in a good rather than a monopoly, prices fall and quality rises. Thus, under polycentric law, law enforcement would be cheaper and of higher quality. So, while it would be protection for those who could afford it, much more people would be able to afford it.
How is it of 'higher quality' if they have no motivation to go after all crime equally? The Police would being even more selective in their enforcement of the law because of lack of resources. Whole neighborhoods would deteriorate almost immediately as a result, and the criminal justice system would become a fractured mess. Plus being able to call 411 and have the police show up regardless of your immediate ability to pay is more convenient and reliable than hiring mercs. Some utilities are government monopolies for a reason.
The United States also had the largest percentage of home-grown anarchists and socialists from 1900-1939 in it's history. After the New Deal established basic welfare people calmed down. In many ways FDR went too far (particularly in regulations), and I'm happy that we've taken steps to fine tune or eliminate programs where necessary. But the overall idea was and still is necessary to keep society in check.