ya it would be. but i'm guessing it's the same reason why Apple music sin isn't yet on Apple TV, and that would be because of copyright reasons.
Even using Continuity, i don't think Apple would want u to listen to Apple music on a different device, but started from another device..
Its crazy.. cos its just streaming... not physical music u have as files...but its probably due to a control type issue with copyright holders as my only guess.