If you’re already using an iOS app for Google Music (I use Melodies), there is a little work-around I’ve found which works. In the web app, you can click “Add Album/Song to My Library” and then re-scan your library in the app and it all will appear.
Granted, in the app you can’t browse for music which isn’t already in your library, but the above steps are definitely doable and definitely Spotify-unsubscribe-worthy.