They are not better or superior people, but they represent the values we should collectively hold as highest, and this is a role and a duty assigned to them.
Unless I'm very, very much mistaken, the way the very few people who end up getting to be the monarch behave and live their lives suggests that they themselves DO believe themselves to be far better and superior people to everybody else.
I can think of no other reason why they would, with a completely straight face, bang on about how passionate they are about sustainability and protecting the environment whilst living as wantonly, opulently and arrogantly as they do.
We regularly hear statistics telling us that we would need something like 4 Earths to sustain us all if everybody in the world lived at the same level of consumption as your average person in a developed western country; how many thousands of Earths would we all need if every inhabitant lived at the same flagrant standard of luxury as the British royals?
And it isn't an inevitability of having a royal system; plenty of other countries' royals seem to manage with living lives that aren't specifically designed to cram their boots with gold at every single turn.