It's as if Apple Music was a monopoly giving it's the default music application same as Internet Explorer was the default browser. I'll bet Apple Music is so integrated into the OS that it would be impossible to remove.
Spotify is the market leader with 31.5%.
Apple Music is #3 at 12%.
https://sqmagazine.co.uk/music-streaming-statistics/
I've deleted the Apple Music app from my iPhone, so you can definitely remove it there.