Unfortunately, the truth is we cannot be monarchists even if we want to be. As commenter Roland on Salo Forum explains,
The monarchists from the New Right do not understand the history or nature of traditional western monarchy. The monarchy to which the mediocre elites in the article above are connected is the institutional foundation of western culture, established by powerful, enterprising men over the course of a millennium through force and intermarriage. Accordingly, the traditional monarch either earned his rights through conquest and usurpation or inheritance from someone who had earned those rights. If those rights had been lost, the only way to reacquire them was by earning them again through brute force. Therefore, we can imagine a modern monarchy that reproduces the political conditions of classical absolutism only to the extent that any modern individual possesses the resources to challenge, militarily, the modern nation state.
The main reason an authentic 21st-century monarch is impossible is that the modern nation-state has perfected the absolutist mechanism of government by eliminating the weaknesses inherent in government by a private individual. While a private individual will never be able to command the mob by appealing to their impulse to self-rule, modern democracies are able to fund and power their absolute, centralized governments by cloaking every policy in the cover of democratic legitimacy (the genius of Hobbes). Moreover, while it took monarchies hundreds of years to acquire the legitimacy of the Church, modern governments can choose when and how their acts will be connected to a given myth by virtue of being premeditated, written -- "founded" -- governments. The United States government is, in fact, the premier example of modern absolutism because it succeeded in adopting some of the classical methods for harnessing and placating the mob without damaging the scope of the absolute, centralized government, i.e., without allowing classical aristocratic republicanism to actually perform its natural function.
People who claim that aspiring and upstart monarchs can do the same are actually thinking of modern, ideological dictators who acquire power by virtue of their ability to manipulate the mob through appeals to justice and other myths rather than by virtue of their personal material success and acumen for war.
The quote is admittedly a secular viewpoint. But where do we even begin to return to the institution of Divine monarchy? To take a single example, England's line of succession is hopelessly tangled by intervening democratic acts. I've previously commented on the morphing of European monarchy into a pan-national, inter-bred ubermensch here. It was for no small reason that the Israelites were commanded, "Thou mayst not make a man of another nation king, that is not thy brother." (Deuteronomy 17:15). (They were likewise commanded, "He shall not have...immense sums of silver and gold," but that's another topic). Not to mention, where are the "true" bishops of the Church to perform the rite of ordination these days--Catholic? Orthodox? Lutheran-Missouri Synod? Any one of hundreds of Protestant sects?
In terms of culture, a paradigm shift that results in the populi viewing their nation and state as legal property of the King is hard to imagine. There is a passage in Neal Stephenson's Quicksilver/Baroque Cycle when Daniel Waterhouse suddenly comes face to face with "England" during the London Great Fire in the exemplar of Charles II, personally directing the firefighting efforts. Can anyone imagine a modern American making this sort of equivocation?
Practically speaking, even if (1) the legitimate bloodlines could be traced and (2) the property restored, the institution itself is utterly gone, reduced, as Taki notes, to a purely ceremonial role. The extant order and all existing public property claims would have to disappear, and some putative neo-monarch start again from Year Zero. Not impossible, but extremely unlikely.
As they say, you can't go home again.