I disagree, there are some divisions of man that aren't arbitrary at all, and being magical or not is one of them. Of course we're aware of the vast capabilities it has, but what good is it to allow muggles the knowledge that magic exists? Nothing they do will grant them the same abilities, and it isn't as though magic is some extraordinary cure-all anyway. It's fantastic, of course, but our world isn't without its own problems.

Wealth and magic can hardly be compared. Money, social status, theoretically these things can be gained, even though some might be lucky enough to be born with both. But with magic, you either have it or you don't.