The problem is that, according to your documentation, local music has to be on a desktop (the only way to listen to local music on mobile is to be connected to the same WiFi of a desktop that serves that music (!)). Which I think defeats the purpose of having your music on the go.

You can still add local tracks to playlists and sync those playlists to your phone. I have plenty of albums that don't exist in Spotify's cloud that I bring with me on my phone as "downloaded" playlists.