I don't have an iPhone. But at least on OSX I didn't find a clean way to remove Apple Music.

Every time I accidentally tap play on my bluetooth headset it opens Apple Music and asks me accept the ToS, which I happily reject. It's a daily thing for me because it's almost impossible to put my headphones on without triggering a play due to bad button placement.

Yep, I have it disabled. My main music apps are “Picky” and Bandcamp, and it works pretty well.

When they do start autoplaying in the car (Picky does it), it’s at least whatever I album I was last playing on the app.