I'd say the grand parent view comes from an uneasiness at anything hereditary, although there's much less objection to hereditary wealth for some reason.

So I'd say it comes from a dichotomy between hereditary wealth and hereditary power, although it's well known that monarchs in democracies are tightly constrained while hereditary wealth brings hereditary power.

It might be the inevitable tie between monarchy and religion which creates a de facto most "correct" national religion. Along with the occasional claim that mythical origins are literally true.

And while comforting, historical and even stabilizing at the moment, it's worth noting that a great many monarchs were quick to join the wrong side of history in WWII.

So, for those without a monarch and the attendant enthusiasm, the institution looks like an extremely expensive and potentially dangerous embodiment of unfairness. Without commenting on the correctness of this view, one can see how it would make monarchies and monarchists incomprehensible to outsiders.