A classy girl might have higher standards but I don't think that necessarily means she's high maintenance. In fact she might be lower maintenance in that she's easier to trust. As long as she's not pretentious , being classy/educated aren't bad traits.
I think most do since most guys think of "classy" as rich instead of behavior. It was sort of like the theme in Great Expectations. It's behavior that determines classy behavior but society doesn't see it that way.