@Joe Nation,
It doesn't matter is you said beneficial, i didn't. You must be really thick when it comes to this subject. Their useful purposes are those i listed--the source of honors, and the non-partisan head of state. I don't understand why you keep asking me to state what i stated at the outset. You may not value those functions, but they are useful nonetheless. People who live in monarchies willingly find them useful for those purposes.
Now, since Fil "I'm nearly incoherent in English but that doesn't stop me" claimed first that this is a tautology (which is nonsense because if it were i'd not have needed to state it) and then that it's obvious, i'll explain what i mean about people who are happy to live in monarchies. Syria has been, for at least two generations, a monarchy. No matter what the Assads have called themselves, they have been functional autocrats. That's a rule by one person, a monarchy. I don't think it's unreasonable to say the Syrians arean't happy about that. Mallomar Gotdaffy was, in the same sense, a monarch. The people of Libya don't seem have been, most of them, too happy about that. Any of the kleptocracies which have been ruled by a single individual for decades are functional monarchies. The evidence at least appears to be that people who live in kleptocracies aren't happy about it.
But many people in the monarchies of Europe seem to be content with having these figureheads as heads of state. To that extent, they serve a useful purpose. Whether or not you like the idea.