That's currently how it works.
This is purely an issue and complaint for when nothing at all was playing or open, and an app hasn't currently registered a handler.
If you land on a fresh desktop from reboot and press play, what should happen?
But whatever, the experience is bad: I have to wait for the Music application startup time, then click the context menu and select "Quit Apple Music". It feels like being forced to watch a product ad. Opening Apple Music is never what I want. Imagine if pressing shift opened TextEdit by default, that would be silly. Or doing CMD-v where you can't paste would automatically pop up some random app.
I feel like no machine response is a correct UX pattern in this case. The absence of sound playback would indicate to me that I need to do something else to play sound.
Whatever is the last thing that was paused should play IMHO. If nothing was paused, it should do nothing. Else, you open a pandora's box of possibly wrong choices that the user then has to close.