Being rare and useful gives something value.
That's a given, though how much? And how much of that value is convention & faith?
That depends on the usefulness and the rarity.
That is however not the question here. The above clearly shows 'backing' is unnecessary. Bitcoin backs itself.
Are you saying Bitcoin's value is due to its rarity & usefulness? In that case, i'll release Bitcoin V2.0 -- identical to Bitcoin in every respect, but with just half the coins.
Go ahead. You'll be in viral competition with the established status quo -- Bitcoin. Good luck with that.