Would you believe that I, as an ancap, also find Rothbard unconvincing?  Not only that, but I don't think the "non-aggression principle" is an adequate guide for political philosophy.  I'm not a libertarian due to moral axioms, but rather, because I think it produces the best outcomes. 

When I talk about anarcho-capitalism, I don't mean ending a govt and leaving a void.  Rather, I hope that certain institutions replace current institutions.  I don't desire lack of security or legal adjudication; I want a market for such.  In place of monopoly, I want competition.  Upon reading this, I'm sure you already have objections, such as, "Why won't various security providers simply fight each other?  Wouldn't they basically be gangs?"  Good question.  Just like you mentioned how at the supra-national level, there's relative peace because of economic development and the high costs of war, in my ideal world, security providers would find peace more profitable than war.  You might be skeptical; I don't blame you.  It's not without cautious skepticism that I hold my views. 

To flesh out these ideas better, there's no better book than The Machinery of Freedom http://www.daviddfriedman.com/The_Machinery_of_Freedom_.pdf by David Friedman.  If you appreciate a beautiful argument and a razor-sharp mind mixed with humility, you'll love the book.

As far as empirical examples, there are examples to various degrees, even if not in totality:

* federalism in the early US
* no supra-national govt at the world stage
* medieval merchant law
* insurance companies having procedures to settle disputes outside of courts
* rural California ranchers (Friedman's more advanced book Law's Order goes into this more)
* as mentioned earlier, medieval Iceland

Let's also recognize that just because something is unprecedented, that doesn't mean it's impossible.  Institutionalized slavery was a human universal... until it wasn't.  Women's suffrage was crazy... until it wasn't.  Democracy itself was nutty (one ancient Egyptian to another "What, the ruler will simply step down if he loses a popularity contest?!?!  Haha, you so crazy!!")...until it wasn't.  The idea of a functional cryptocurrency was crazy... until Satoshi made it work.

So yes, the list of functional ancap societies in the modern area is blank, but that doesn't imply they can't exist.  What matters is--can societies thrive under such a system?  Can they evolve into such a system?  The reason I call myself an ancap is because I believe, cautiously, that the answer to both questions is "yes".