I imagine a word where we have about as many monarchies as we have counties in the USA. But globally. Tax would be more voluntary with such small geographic landscapes. Freedom of movement exists. People will organize naturally. Those monarchies that opress their people will fall in short order.
Why bother having a monarchy at all, then?
That's close enough to anarchy that I don't see any point in making a distinction. Anarchy would just be that, but on an even smaller scale. It doesn't work without property, and if you can own a few miles and pass it on to your kids, then you might as well invent some titles and call it a monarchy.