Isn't the play button issue solved by the Touch Bar? (I don't know because I don't use Apple Music yet), but I'd assume so since:

I just started playing a Youtube video and a Spotify song, then clicked on the audio button in the Touch Bar and it looks like this, double clicking the icon opens the appropriate app (opened that through the Control Strip, enabled in the Keyboard settings): https://ibb.co/6Pr1V6x

Though I guess the point is moot since the Touch Bar seems to be being phased out, and also due to the existence of 3rd party apps...