The question is somewhat misleading. A private law society requires a homogeneity of interests, and therefore is a small society. An argument in favor of a private law society is an argument in favor of many small societies (private cities). Since society’s ills are largely the product of the opposing vales of credit at scale, but diversity of interests at scale, we generally need governments to resolve conflicts between groups with competing interests, all of whom dislike compromising, but all of whom benefit from the insurance value and credit value of a large government. What is important here is that Hoppe has solved the problem of large monopolistic bureaucratic government acting as an extortionary, self-interested monopoly insurer maximizing it’s profit for employees, with small cities and competing insurance companies. That this is advocating a return, en large, to the pre-empire german city states, is probably not lost on historians. It isn’t lost on Hoppe.
So it is a reasonable solution except that the value of credit to large populations is that they can finance the wars necessary to keep other large states at bay. This is where the banking and fiat credit system as we understand it comes from: the finance of the wars of napoleon and britain. Which is one of rothbard and hoppe’s reasons for trying to undermine the large monpoly state: is that it is used to finance warfare. However, if the USA uses it to finance warfare, that means europe can use it for social programs, because europe doesn’t have to. The US then sells enough dollars as petrodollars to pay for its military, and then inflates the debt, effectively charging these countries – and the whole world, for the cost of its military.
I hope this helps put such things in context.