I think that Rothbard and Friedman are basically discussing different things.
Rothbard is discussing morality and what the law should look like according to his view of morality, based on his definition that anything that furthers people’s basic natural inclinations, including survival and cooperation, is moral. As pointed out, he does not discuss what the situation would be in a poly-centrist legal society where many parties had different views of morality, only how conflicts would be solved in a society where everybody held his views.
Friedman is not discussing morality at all. He discussed what poly-centrist legal society would look like. As far as I understand, he doesn’t have a view of objective morality, nor does he think we can arrive at one. I don’t think he is a moral nihilist or subjectivist, but more of an intuitionist.
I think there is a third view which neither of them holds, and that is what seems to me a version of contractarianism: it describes what morality and/or law ought to be if their goal is for people to cooperate with each other. This view describes what law ought to be if the goal of the law is to reduce conflict.
My problem with Rothbard’s view is that it assumes human nature to be something specific, and derives from it what human goals should be. But every human’s nature (and, therefore, goals) is different. Furthermore, it doesn’t justify why following human nature should be the greatest ought.
My problem with the contractarian view (or what I described as contractarian) is basically the same — it assumes that all people desire the same from the law: peaceful resolution of conflicts. But maybe people want to live in a society where there is a certain degree of violence, but there is protection of what they consider to be moral? For instance, a libertarian fundamentalist Christian has to decide what he cares about more: the fact of the government’s aggression or that people are prevented from committing sodomy. There is no good objective reason why he should abhor the former more.
My problem with Dr. Friedman’s (and contractarian, to some extent) approach is that it doesn’t explain what our preferences ought to be. I.e., why should I prefer the free society? For greater utility? For greater freedom? Is it implied that my intuitive morality should place freedom as the top preference? Why?
The same is with NAP: before one defines aggression, one must define property and, most importantly, justify his definition. Both Rothbard’s and Hoppe’s defense for their view of property seems to me to have holes and question begging. Dr. Friedman doesn’t have any coherent definition of property (but then, he doesn’t care about NAP).
Contractarian approach seems to me to be the most straightforward in that it suggests that we ought to define property in such a way as to minimize conflict (which suggests homesteading and self-ownership), but, again, it’s not clear why people ought to place conflict minimization as the priority in what they expect from law and property definition. (Some may want artists rewarded for their work more than to avoid conflict. I want to make sure that children are protected from abuse before they become adults, but that I also get to eat animals. I am yet to see a coherent, contradiction-free explanation of how our definition of property should protect children but allow us to use animals to our hearts’ content.)
So, overall, Dr. Friedman’s theory seems to be the most coherent, but then it simply avoids the question of what we should consider as property or as moral today. E.g., if I lose my phone and someone finds it, ought he return it to me? Rothbard may have a clear answer to the question for everyone. But Dr. Friedman would presumably say: “Today, do what your intuition tells you. In the future, probably the same, unless the original owner discovers that you kept the phone, in which case your protection agencies will figure it out between themselves.” But also, because there is no moral justification of one legal view over another, Dr. Friedman’s legal universe is basically a nuanced version of “might makes right”, with the addendum: “if it’s economically feasible for it to do so”. That may be a good description of how things will be, but not a good description of how things ought to be, unless one is a utilitarian.