Of course. But how is this an argument for a monopolistic legal system?
Remember, the fundamental issue is competition vs. monopoly. Monopolies are inherently rights-violating (and hence are immoral) and face information and incentive problems (and hence are inefficient). Markets, on the other hand, can exist without aggression and have a more effective incentive structure. Therefore, a competitive legal system is preferable to a monopolistic one.
I notice minarchists often argue against anarchism by asking how some specific scenario would be dealt with under anarchy, and then, unconvinced by the response, conclude that anarchy is undesirable or absurd. But these types of questions are irrelevant: the anarchist has no burden of proof to show how specific scenarios would be handled. What they do have to show is that the incentive structure of anarchy is superior to the incentive structure of minarchy. And this they have done decisively: market competition has a more effective incentive structure than political democracy.
Unless the minarchist can come up with a reason why the legal system should be excepted from this rule, they have no choice but to abandon statism and accept anarchism.