Honestly, my biggest issue with the "must be descended from a Monarch" rule is that there are a LOT of people distantly descended from ancient monarchs. Charlemagne was kickin' it from the 750s-810s, and had a whopping TWENTY children. Average length of a generation is about 30 years. So we'll call it 40 generations. That's a
lot of people. Even if you're only counting male heirs—even if half of each generation dies without bearing children—you're talking about hundreds or thousands (or hundreds of thousands) of people (remember, they're Catholic) who are "descended" from royalty. Let's even say that the Black Plague reset the family tree all the way back to one heir; you're still talking about tons of people. And in checking my math, I found this Wiki article about it:
https://en.wikipedia.org/wiki/Royal_descent They even list Charlemagne as an example. The further back in time you count, the greater your chance of being descended from a monarch (and, incidentally, if Michael's descended from Charlemagne, it's entirely possible he's also descended from William the Conqueror more recently, which ties into my whole "Hastings is super important" line of thought).
I'm lucky in that my great grandfather was a genealogist, and his Magnum Opus was tracing my family's history as far back as there were records. My lineage has been traced back to 1066 (which may be why I have such a hard focus on Hastings) to the Doomsday Book. Turns out I'm descended from Barons. Now, my family was staunchly Protestant and fled to America in the 1630s, so you're talking about 1-2 children per generation (and lots of my family tree died as young men in conflicts like the American Revolution (yes, I'm a Son of the Revolution) and the American Civil War), so there aren't very many of us left.
I mean, 16 million people (.5% of the world population) are descended from Genghis Khan, right? Toss one of those a Sword.
Anyway, the point I'm making is that, in reality, it's not all that special. There were lots of monarchs across the world over the past few millennia, and lots of them had lots of kids. One report says that basically every native British person is descended from royalty at some point, if you go far enough back.