Devin Finbarr asks in the comments whether I'm talking about hereditary or elective monarchy.
The answer is that it is hereditary monarchy that I have in mind. The problems with elective monarchy are, firstly, that it introduces politics to determine the succession. The electors can demand commitments from the candidate that would divide his power. Secondly, it reinforces the damaging idea that the monarch is a "Servant of the people"
The monarch is not a servant, not quite. A monarch is responsible for the well-being of his people, but he is not responsible to his people, or any subset of them.
Rather, I follow Filmer in seeing kingship as an extension of fatherhood. It is clear that a father is responsible for the well-being of his children, but he is not their servant and he is not answerable to them.
Exactly what he is responsible to is not clear — to his ancestors, to his descendants not yet born, to both (to his genes, perhaps, in a modern view of that). Maybe just to himself or to his conscience or to God. (Inevitably, the modern state makes parents responsible to the bureaucracy for their children, with predictably horrific results).
Back to succession, there is a case for giving the monarch the right to choose his heir, rather than going strictly next-of-kin. That involves no division of power, and seems to be a way of weeding out some of the less capable specimens. Against that you have the danger of weak elderly kings being pressured, or of ambiguity.
In any case, it is important to remember, when talking about whether monarchy should be like this or like that, not to miss the point. If we could sit around a table and design a constitution that would be magically enforced, we could do a lot better than monarchy. Monarchy is a natural phenomenon that happens to a society, not something we engineer. The reason for discussing it now is to encourage people to accept it, if and when it happens, rather than to fight against it as modern fashion would dictate. The small print will have to take care of itself.
Incidentally, the "perpetual motion machine" analogy that Devin liked, like so much else here, is due to Mencius Moldbug. I like it chiefly for the resemblance between the designs attempted by enthusiasts to achieve either perpetual motion or separation of powers.