Hero might be the wrong word except in the traditional sense of demigod. There's an implicit positive moral judgement in the term that being a monarch has very little to do with.

I'd also argue that it's more that monarchy by its own self justification is based on the idea that the king protects, and therefore effectively owns, his subjects. A king might do that by effective governance however. If they can't do it personally they'd need the loyalty of a champion, for example.