Well, for one possible answer: I personally don't want "music that I have added to my library by ripping or buying digital files of" and "music that I have added to my library by clicking 'favorite' in a streaming music service" to be separate libraries. "Okay, I want to listen to a song or two from the most recent album by The Black Keys, so I'll go to this app, but now I'd like to listen to ELO's Greatest Hits, so I'll go to that app." I just want to say "I would like to listen to my music."
That's nice if you actually subscribe to Apple Music. As it stands, searching your library in Music.app returns results from Apple Music, with ~3 extra taps required to see the results from your own library, and often the inability to even navigate to a result in your own library if it matches the name of a title that's been delicensed from Apple Music.
Did you try turning off Apple Music in Settings? I just did that, and all mention of Apple Music goes away from the Music app, including in the search results.
