Why does this Wired author assert that "You can't delete" Apple Music? If Brian Barrett means "you can't go back to the old Music App", he's pretty wrong. If he means you can't delete the Music App period, he's right but that has always been the case. And I'm pretty sure he means the former as he seems to be lamenting the change from the old Music app.
For those who don't want Apple Music (I didn't - I was spooked by the lost songs/mixed up metadata problems and didn't think it likely I would use Connect), and who want to revert back to the old pre-Apple Music app, do the following:
1) go to settings>general>restrictions and scroll down to "Apple Music Connect". Deselect Apple Music Connect and enable restrictions.
2) go to settings>music and deselect "Show Apple Music".
3) if you use iTunes Match, leave "iCloud Music Library" enabled to keep playlists synced and all music available on your devices.
And now you are back to your pre-Apple Music app. No Connect. No "New". No "For You". Just Music, playlists, and radio. Just like before.
Is it a little inconvenient? Absolutely - I needed to write a set of instructions. Is it difficult? Not really, the instructions had two (maybe three) steps.