No native music app

Other download services seem to be able to manage to sell the right to listen to music without restricting how and where the user does so

I suspect it is more about keeping track of what the user is listening to so they can monetise that information.
 
Which download services are you referring to? The pitfall of allowing that is if a user decides to download a crapton of music, and then cancels their subscription. Then they'd have a load of music that was virtually "free" (not counting the subscription fee -- unless this was done during a free trial, in which case it was free). That's something most if not all legitimate music services (as well as recording labels) would want to avoid.
 
Amazon for example.

Amazon only downloads MP3 files of music you actually own from them, like music you buy from them directly. Their streamed music service encrypts the music they download as DRM files and you cannot use them with an external player. Their files are not listed by name for music you do not actually own and music that you own that you download goes to your music folder, whereas music you just stream and download from their service but do not own is stored in another part of the android file system.

I have downloaded both types of music from Amazon which is how I know this.
 
Another vote for Poweramp for locally stored music. I cache music with YouTube Music for offline use.
 
Amazon only downloads MP3 files of music you actually own from them, like music you buy from them directly. Their streamed music service encrypts the music they download as DRM files and you cannot use them with an external player. Their files are not listed by name for music you do not actually own and music that you own that you download goes to your music folder, whereas music you just stream and download from their service but do not own is stored in another part of the android file system.

I have downloaded both types of music from Amazon which is how I know this.
I also know this. Look back and you will see I explicitly talked about buying the right to listen not renting it.
 
I also know this. Look back and you will see I explicitly talked about buying the right to listen not renting it.

Ok, fair enough. (I thought we were talking primarily about streaming services.) I agree that purchasing music tracks outright is pretty much your main alternative (apart from ripping tracks from CDs or other physical media).
 
You were talking about (subscription) streaming services. I have always been talking about the alternatives which better suit many people.