It should be glaringly obvious the "libertarianism" of the variety espoused by the Murray Rothbard/Robert Nozick/Ayn Rand axis most definitely resembles feudalism. I can get into detail if need be.
I'd be interested in reading the details. Just an overview with a few significant points supported by a supporting detail. Nothing too long, but a classical essay style would be a welcome relief from all the "I told you.."s and sweeping overgeneralizations.
I'd like to preface this by stating Robert Nozick differs in many ways from Murray Rothbard, and Murray Rothbard represents more of the contemporary libertarian movement in the US.
Most of them want to dismantle the modern nation-state. What is the government for the Libertarian? It's essentially privatized, consisting of private contracts, and the ultimate goal being the privatization of arbitration and protection services, whereby political power also becomes exclusively privatized. The protection of your rights are then commoditized: protection of said rights are based on one's ability to pay, based on private authority in the form of contracts.
What's the problem with this arrangement? There's no type of public power which can act in an impartial capacity. There also isn't any type of legislative scaffolding which is answerable to the public in any type of non-market form. We'd have zero equal rights in such as system. We're talking about feudal, private governance in such a system. In such a system, political power is acted on for private ends, not toward the public good in any way, shape, or form.
We can get into their market delusions later on at some point.
The problem with your theory of course, is that government itself rarely acts in an impartial way. And that problem is getting worse, not better.