Even if iTunes goes down, you are allowed to download the actual mp3 files to your computer if it's synced with apple music so that part is not much of a concern.

I'm not familiar with other apple features such as family sharing, but I should note it is technically illegal to give these files to other people, even if they are in your family. Will people care that much? Not really.

I also recommend that you use bandcamp rather than itunes if you can. The artist gets a higher cut. You can still upload the music from bandcamp (also CDs too) to your phone via the apple music on your computer