AirDrop is implemented in specific apps, and exposes specific files/types. It's not a option in Music, and since audio files are silo'ed, no other app can AirDrop them either (on the latter point, I'm also assuming AirDrop is exposed in the public API in V5 SDK/XCode).
It's not a technical limitation, but a policy decision, and I think the OP is right on with the concern over copyright. I'd image other players like Amazon wouldn't allow this either.