Here is a sledgehammer solution. It works for me, because I use iTunes Match. I don't mind wiping all music from my device because it will download when I play a particular track.
1.Go to Settings
2. Go to General
3. Go to Usage
4. Wait for Storage to load
5. Go to Music and swipe
6. Delete will pop up
7. Press Delete
This will delete ALL songs, but will not remove the music app.
There you go.
Great news, I don't know when it came back but you can now delete an entire album / artist from your iPhone in one action.
Just go to the album / artist list, and for each of them that has local tracks, you'll be able to swipe left and press delete. That will remove the songs from your phone and keep them on the Cloud if you use iTunes Match.
To be even faster, you can go in Settings / General / Usage / Manage Storage / Music. There, you can still swipe left on artists / albums / songs to delete but only local tracks will show up there. It could easier to clear your library.
Hope this helps !