many monarchies are hereditary celebrities rather than hereditary leaders, where the position is kept around for the tourism value and they do not have (or claim to have) any right to rule over people

There is some power, although due to it not having been exercised for a century. Lawyers argue the legal texts are no longer binding.

But they’re ultimately the last entity that should block a party, if they turn full on authoritarian. All democracies need a non political entity, to overlook the democratic process and stop undemocratic moves.

Finland has a president for the same reason, and likewise does several other European nations.