That is not a claim that the free market doesn't work. The free market works fine, as long as no one has a monopoly on defining what is true or what is just. Letting a private business or individual have a monopoly on deciding what it may rightfully do doesn't work, regardless of whether the monopolist is a state or a street thug. That's why the free market is superior: It denies monopoly power, and gives customers choices about which car to buy, which house to rent, which school to attend, which independent Rights Enforcement Agency to use, and which independent arbitration service to use.
That is not a claim that the free market doesn't work.
Of course it is.
"Letting a private business regulate/police itself" is the exact opposite of the oppressive regulation and confiscatory taxation regime...which is what we have now.
AKA: A market-adverse environment.
What is an "independent Rights Enforcement Agency"?
Please give an example.