remove all songs from iPhone that aren't in any playlists via iTunes
How about only syncing the playlists you want instead of the entire library in iTunes (or Finder if your computer is macOS based)?
If you are someone that learned to drive a car without an automatic transmission, your method is akin to manual shifting. You could also enable Apple Music or iTunes Match and then you no longer have to micro-manage which I played songs get removed as your device keeps track and cleans automatically when you run low on free space on device.