So a monarch that can’t appoint their own heir really isn’t much of a monarch. The point of being a monarch is not being beholden to any rules.
This is just an oligarchy with rules that don’t benefit 3/4th of the participants–which is as odd as it sounds.
After all, the point of 4-5 year terms in modern democracies is that you don’t have to wait your whole life to take over.
It’s an interesting concept, but coming to this arangement–and maintaining it in perpetuity–must have been an extremely extrordinary set of circumstances.
Is the monarch required to be sacrificed every so often? That would kinda mimic the Aztec Festival of Toxcatl, where an impersonator of the god Tezcatlipoca was sacrificed every year after being treated like a god for the year. The god-man was usually selected from royal families. He had religous function and was provided for in specific ways (eg a harem) but he wasn’t a monarch.