Apple seems to have done this with the podcast app already and now I'm expressing the same issues as you I have all the music downloaded.
With the podcast app, you need to go online (by enabling cellular data in the app settings), start playing, and then go offline. i've already checked data usage and it doesn't download anything. It simply refuses to let you access locally stored podcasts.
it seems to be the same for music now.
For the music, it's mine, except for the stuff that I bought from iTunes which I guess is "licensed". I purchased it. Either it was loaded from CDs that I purchased or I purchased it through iTunes. In fact, some of the music was made by myself or friends. I can't shuffle or play a playlist of that offline now by pressing those buttons in the playlist view. It seems like they're slowly taking away features and trying to migrate people towards Apple Music subscriptions. Again, they did that with the podcast app and it's still in that state...
So, unless it's a bug that they accidentally introduced, this seems like it's a new feature.
Personally, it's frustrating to see more and more taken away, even if I'm purchasing things properly through the iTunes store. I will never be interested in streaming music and there's no reason for me to be online to listen to local music.
But, there's a much larger issue here:
Often times I'm not within cell data areas and don't have wifi. I absolutely want my music local and playable.
I'll probably be looking for new apps to use for these now. :/
It would mean a lot if a pro, Apple support (Linc, you still around?), or other "in-the-know" individual can help out.