I realized (some time ago) that I tend to use "have fun" as a goodbye, especially if I know what the other person is doing. If I don't, I tend to use "see you".
There's probably some psychology and philosophy behind it, something about the purpose of life is to be happy (but with restraints like not directly decreasing other's people happiness). Or maybe it's just because I wish I was having as much fun as they're having.
Nah, I think the first explanation is better.