Honestly, I don't really see this changing much at all.
The stage demos for their new radio show were examples of exactly why I stopped listening to radio.
At this point I think most people know whether they want to use a streaming service or not.
For me, I just don't see the value in paying for a service which streams lossy music. I'd use a service like that if it were free - or perhaps significantly cheaper, but I'm not going to pay a subscription.
The only exception to that is that I might pay for the minimum term (typically a month) if I'm going to be hosting a party and I know that it's going to be the type of event where people will want to queue up music they want to play, rather than putting on a selection of music from my own library.
A few months back we were planning a birthday party for someone and we all collaborated to a couple of different playlists on Spotify which worked out perfectly.
It was good party music, but I only had maybe 10-20% of the songs in my own collection - and though it was fitting, there was certainly a lot that I wouldn't want to own a copy of.
At the same time, it did get me to purchase a couple of new albums as well, after really liking a few of the tracks.
All I see Apple Music doing is taking people away from Spotify, especially with that $15 family plan.
That seems like quite good value, if you don't mind paying for lossy quality. (and I know most people don't)
For the rest of us who are concerned about music quality, I think we'll continue to purchase music and use software like Media Center to manage our own libraries.
It starts to become a threat once they're streaming lossless CD-quality music at reasonable prices (i.e. not twice what everyone else is charging right now) and we can create our own "local library" from the selection, rather than browsing an infinitely large collection.
But I don't really see that happening any time soon.
What I actually think would be the best "solution" for now is setting up
TuneAero (or similar) to forward AirPlay music to the WDM Driver, so that you can play to Media Center via Apple Music, Spotify, Qobuz, Tidal, or any other preferred streaming service.
After all, aren't most people that want to use streaming services doing so through their phones?
For me, Apple Music wouldn't replace Media Center as the "server" it would replace JRemote as the "remote".