Democracy vs Monarchy

I keep hearing the stupid argument a republic isn’t necessarily more democratic than a monarchy (because North Korea). Well, isn’t the whole definition of a monarch someone you DON’T vote for? Okay, you can take away almost all the powers of the king so that he’s just a figurehead, but then, what’s the point? Either the king has power, in which case it’s not democratic, or the king has no power, in which case he’s a waste of money.