As somebody who enjoys listening to beatmatched DJ mixes, I'm glad I don't have "perfect" pitch. I'd hate to have vast amounts of music sound "wrong" just because the speed and pitch was changed slightly to synchronize it with other tracks.

Relative pitch is very important for musicians, but absolute pitch is mostly useless. The only use I can think of is singing songs with a cappella intros, so you're in tune with the instruments that come in later, but even this is of very limited value. In a casual setting you can just play a note on an instrument before you start, and for a professional performance you're going to have IEMs that can play the reference note for you.