I've just done these suggested solutions (which worked) on my iPad Air and I'll bet this "problem" is a silent strategy by Apple to make it difficult to use your own physical music files library (ripped from your CDs, Amazon downloads, etc.) and to encourage exclusive use of AppleMusic. Am I being paranoid? As an added bonus to having checked the "Manually manage music and videos" function, it also made my whole iBooks library disappear from the iPad. I have quite a few books in iBooks and it's a total tactical nightmare having to resync them all.