Hello OP.
>What legitimizes a monarch?
For myself, there are two answers. The first is probably the answer I rationally accept, and the second is probably the answer I emotionally accept.
First:
Do you really want legitimacy? If you want a limited government, legitimacy is not something you want government to be perceived as having. I don't think monarchies are 'legitimate.' But, I also don't think that any government is 'legitimate.' Which is the benefit to a monarchy. Any governmental system isn't all that different, the only difference is the smoke-and-mirrors to which they make people 'believe' that they hold the power (when really they don't). To that end, at least in a monarchy people have the truth. And because of that, historically a monarch couldn't get away with very much taxation at all, least of all any egregious form of direct taxation.
On a personal level, I like monarchies just because it blows away the smoke-and-mirror games and politics and makes it clear to me what I can really do and what's honestly within my abilities to change. Hoping that one can make a change through spending the enormous amount of time in campaigning and running a PAC or making a political party or something like that is a fool's errand. When those options are closed off, it's much more clear what you can really do to better your life (move, bribe, assassinate, etc.).
Second:
Oddly enough, Rothbard's argument AGAINST monarchism.
>Let us say that Ruritania is ruled by a king who has grievously invaded the rights of persons and the legitimate property of individuals, and has regulated and finally seized their property. A libertarian movement develops in Ruritania, and comes to persuade the bulk of the populace that this criminal system should be replaced by a truly libertarian society, where the rights of each man to his person and his found and created property are fully respected. The king, seeing the revolt to be imminently successful, now employs a cunning stratagem. He proclaims his government to be dissolved, but just before doing so he arbitrarily parcels out the entire land area of his kingdom to the “ownership” of himself and his relatives. He then goes to the libertarian rebels and says: “all right, I have granted your wish, and have dissolved my rule; there is now no more violent intervention in private property. However, myself and my eleven relatives now each own one-twelfth of Ruritania, and if you disturb us in this ownership in any way, you shall be infringing upon the sanctity of the very fundamental principle that you profess: the inviolability of private property. Therefore, while we shall no longer be imposing ‘taxes,’ you must grant each of us the right to impose any ‘rents’ that we may wish upon our ‘tenants,’ or to regulate the lives of all the people who presume to live on ‘our’ property as we see fit. In this way, taxes shall be fully replaced by ‘private rents’!”
I know Rothbard's response to his own hypothetical. But emotionally I find his hypothetical more of a convincing case for monarchism than his arguments later to dispute this. If you really wanted to argue about the ethics of land theft when you could invariably get into incredibly muddy waters studying the history of deeds-especially on the American continent–then I could see such a shell-game by an astute King of Ruritania working. I mean, fundamentally monarchy works off of a principle of inheritance, and thereby property rights anyways, so…
>how would you bring about your style of monarchy to the USA or whatever state after a presumed balkanization?
The second answer I gave was essentially rooted in property rights, and so is my answer here.
The Grand Duke of Luxembourg started out as a guy who bought the land on top of a very important and strategic hill from a nearby monastery, and then he built a house there. Over the next several centuries it became the Great Duchy. I would suggest something similar. This, of course, means that the United States would become a much more fine patchwork quilt of very tiny countries. Of course, I don't think that's a bad thing.