The issue is more what is the source of law and authority, regardless of the form of government. Democratic republics tend towards the understanding of law articulated by b-chan "vox populi, vox dei". The "will of the people" is supreme. This is theologically unsound as it denys the effects of original sin which darkens the intellects of men not to mention the power of modern propoganda which reduces all issues to sound bytes for consumption by the lowest common denominator. Law must be understood as antecedent to government - this idea is even expressed in the US constitution, tho I am not a fan of that document or it's theory. In the Catholic monarchy and even in the Protestant and "absolutist" variants of the 17th thru the 19th century the King was beneath the law. As de Jouvenal wrote in On Power...
This is a very rough paraphrase granted, I don't have the text in front of me. The point being that Kings had no more and no less rights than everyone else, they were held under the law the same as every man because law was eternal and immutable. The Kings of the ancien regime acted as judges, applying the law case by case not creating it out of thin air as legislatures in modern democratic republics do.
I interpet the writings of Leo XIII in Diturnum and Immortale Dei to mean that any society which recognized the immutability of law and conformed its actions to the natural law would be legitmite in the eyes of the Church. Which virtually every Pope upto and including Pius XII weren't strongly pro-monarchist. It is undeniable they certainly were.
I object to the modern (and largely American) idea of linking democracy with freedom as if the two were inseparable. I would argue precisely the opposite, never in the history of man has the state had so much power over the lives of it's citizens than now in this age of "freedom and democracy". The illusion that "we are the government" causes us to overlook the most egegrious violations. No monarch in history would have dared confiscate 40% of someone's earnings, presume to have the authority to print fiat money, indoctrinate the children of their subjects in "state approved circulumn" or reach into private homes and remove the children "for their own good". We live in a totalitarian society and most don't even know it because they labor under the illusion that "we are the government".
Finally we have the ridicoulous notion that somehow a democracy that elects a monster can suddenly and retroactively be considered not a democracy. So the Weimar republic that elected Hitler was a democracy one day and not the next??
There are a thousand other arguments for monarchy and interestingly virtually none for democracy
I don't think I or anyone else said that it did, though I do agree with Jeff Culbreath that "no Catholic can be an anti-monarchist" in the sense of believing that all monarchies everywhere ought to be abolished.
Thanks as always for your excellent points.