Reading Richard Spencer's criticism of John Médaille's form of "egalitarian monarchism", I was initially moved to leap to the defence of Médaille. There is indeed a sense in which the advantage of Monarchy is its egalitarianism.
What I mean is that the modern democratic state shares many of its problems with the feudal societies of the first half of the last millenium. Power is divided between many competing blocs (in the old world, aristocratic families, in the new, agencies and guilds) whose domains are variable and unclear, and much of what passes for policy results from conflicts between them for power.
The medieval problem was solved by the growth of Royal versus aristocratic power. The Tudors and the Bourbons (for example) were able to dominate the aristocracy.
This can be seen as an egalitarian reform -- the vast power blocs weakened, and the ordinary subject becoming more equal, at least in terms of political power, with his Lord who, like him, is under effective authority.
There are many institutions that today have too much power. A true royal restoration would make the government agencies, the quangos, the media, the universities, the unions, the banks, all bereft of political power. Opinions may legitimately vary as to which of those bodies most urgently need their wings clipped, and the Steel Rule means that I do not assert my own view, but the point is not so much that they all will be subservient to the Sovereign, as that he will be subservient to none of them.
One of the most important characteristics of personal power is that it is the power to get things wrong and then fix them. I do not in fact have confidence in the wisdom of some randomly selected King to know which of the above groups perform useful functions, and which are parasites perpetuated by their own acquired power.
I do think that only personal power is a recipe to eventually find the right answer -- all forms of collective decision-making are too easily swayed by the subjects themselves, with the result that the first decision made becomes irrevocable.
So, to summarise, the advantage of more monarchism, either in the hypothetical future or in the 1500s, is the stripping of power from the oppressors, and that can be (though I certainly wouldn't insist on it) seen as a kind of egalitarianism -- even as a kind of democracy if you really want to stretch.
Unfortunately though, Médaille is still utterly wrong. Actually looking at his pieces on Front Porch Republic, he makes an argument not for the ruling monarch of the later middle ages, but for the very confusion of competing political power groups that I see as analogous to the current mess, and which was superseded by what he calls "Regalism".
Once terms like "Tyranny" start to be thrown around in American publications, it becomes necessary to look at what the issues were at the time of the American rebellion. The rebels were certainly not out to free themselves from an absolute monarchy, since no English King had held such power for a hundred years. The Whigs had first made an alliance with William of Orange in order to remove the Stuarts, who were the last Kings who even aspired to really rule England, and with the importation of George I and his reception at the docks by the dignitaries of the Kit-Cat Club, the alliance became completely one-sided and the Whigs established their permanent dominance. (All English politics since that date has consisted of conflicts among Whigs, with the term Tory being revived from time to time by more radical Whigs as an insult to throw at their less radical colleagues).
George III did attempt to re-establish some kind of Royal power, though I am not sure he set his sights as high as the power Charles II had, let alone that of Elizabeth. (If I find out he did, I will adopt his banner as mine). The American rebellion was the Whigs' way of putting him in his place. The small gains he did achieve mostly lasted into Victoria's reign, but were finally expunged by the advent of universal suffrage and the acceptance of purely democratic theories of government in the 20th Century.