Switching off cellular data in Music does not prevent everything else from happening any time you are in an area where there is a WiFi available and your phone logs on. All it does is prevent any use of chargeable cellular data downloads.

If you haven't looked at Apple's Music offerings, you should. I started out buying albums and tunes from Apple because it was easier and cheaper than buying a CD or vinyl but I have since switched to subscribing to the music. One month's subscription costs the same as a single album and I sometimes add three or four or more albums to my library in a single month, so I am saving $20 to $30 or more each month by subscribing. I can then stream the music when I have WiFi and/or download it to play when streaming is not available or the potential cellular data cost is too high. I have some old out of print albums that I have uploaded and to my surprise, not only are they in Apple's Library, their copy is far superior than what I uploaded. Music recognized the album as being in their library and uses that rather than wasting my iCloud disk space storing my inferior transcription.

I honestly have no idea why your iPhone playlists go away unless you have removed the tunes in the playlist from your iPhone. If you ant to pursue that further, start with this:
  • go to Settings > General > iPhone Storage —
  • How much storage do you have?
  • How much storage have you used?
  • Scroll down the list of apps and find Music —
  • What is the size shown for Music?
  • Touch Music —
  • What is the size shown for Documents & Data?
  • What is the size shown for All songs?

Make intentional errors —
Otherwise the Great Spirit realizes you have fulfilled your purpose on earth.

— Navajo saying