The delete you are describing is to delete something from Now Playing, not a Playlist. Not sure why that doesn't work for you as it works on my iPad. What I would like to do however is use my iPad to delete something from a Playlist which is different from Now Playing.
I'm stunned, you are right! But how unlogical, to me at least. There is no mention in the screen that we are looking at what is Now Playing (to me it is simply the album I have chosen). More importantly, at the top you can load Load a Playlist. So, when you swipe and get the option to add to a playlist, I assumed that delete meant you were deleting it from the playlist. It does disappear, but in the previous screen it is still there. What you wrote explains that. Still, no solution for why you could not delete a song or a playlist entry.
The Now Playing concept has always escaped me, by the way. I simply don't see a use for it. But never mind that.
Being able to delete a number in a playlist or a song altogether from the library, is what I am after.