It costs billions of dollars to enter the market on Law or Justice.
It costs less to immigrate to a member of the oligarchy on Law and Justice.
Most cannot afford the first.
A significant portion cannot even afford the second.
Republican Politicians are rarely right when discussing Patriotism.
Most people can't afford to start their own restaurant, either. Does that mean that the food service industry is fundamentally flawed?And besides that, there is some variation in law between different states and between different cities. Moving out of the country is the only way to avoid some, but not all, US laws.
But to make a more serious point, perhaps some things simply don't lend themselves to competition. Clearly this is true for some industries with economies of scale. But I would argue that it's true for law and justice as well. These two concepts are universally applied. We can't have some nuts start their own country in the middle of the US where it's OK to steal, rape, and murder.
Part of being able to enter a market is access to consumers. A significant portion of consumers of Law and Justice cannot change providers because moving is too expensive. Hence there is an enforcement of the oligarchy.
One example where the US Government has it right is in the market of business contracts. Specifically it does not prevent private sources of Arbitration. This competition in the market of Justice on business contracts has resulted in the private sources innovating superior methods of justice on these contracts and thus private arbitration is the major source of the Justice on business contracts.
However you brought up a very good point on the economies of scale. As seen in the Arbitration example some sources of Justice would have sufficient diseconomies of scale to create sufficient long term competition. This may or may not be true for other sources of Law and Justice. What I can tell you is that Government can through deficit spending ignore diseconomies of scale until the populace revolts.
Also Law and Justice need not be universally applied. There would be intragroup Laws and intergroup Laws and intragroup and intergroup Justice. People would belong to many groups each with there own set of Laws and/or Justice.
I would be perfectly okay with a territory where Stealing, Rape and Murder were legal provided the residents of that district agreed to that lack of Laws. I however would make sure that my community increased the penalty for kidnapping across that border including jurisdiction to follow a kidnapper back across said border.
However each of those is bad terms to use.
If Stealing is legal then legal property rights do not exist therefore it is communal property not theft. This is actually a basis for Anarchocommunism.
Rape/Murder is defined as at least partially non consensual hence the only people who would agree to the lack of such a law would be a Rapist/Murderer. If Rapists/Murders agree to only rape/murder each other then I am unsure if it would be a bad thing. Everyone in that community agreed to the risk of rape/murder so is it still non consensual?
If an activity needs to be done then is there a more valued alternative?
If there is a more valued alternative then does the activity need to be done?
Consider a private company running the fire department or the police department. How can a fire department be profitable? Should people be charged every time their building catches fire for the cost of extinguishing it? Do you like the idea of private contractors acting as police officers? What about the military? Should the US military be completely composed of Blackwaters (now Xe Services)?
Have you heard of Lighthouses? Did you know back before all this technology and radar there was a concern that it would be impossible to charge the right ships because the light from a light house was not able to be sent to one ship but not another. The private market found a solution while the public nature of light still existed. (now "light" from lighthouses can be made private as radar signals but there was a more primitive answer that worked prior to then)
As for Fire departments the common anarchist answer to that is Pay as you use and or Contracts like an insurance.
Do I like the idea of private police agencies? Yes provided diseconomies of scale.
Anarchists tend to promote passive military so using Blackwater and other Mercenary agencies as a defensive army would work fine provided diseconomies of scale.
I personally would concede that if an anarchy version of a submarket would cause a worse monopoly than a government then that is a suitable role for the government to take until innovation removes the problem.