I deleted /home/user/Desktop because I don't put anything on the Desktop.
Unfortunately the directory keeps reappearing.
What I tried so far is to replace XDG_DESKTOP_DIR="$HOME/Desktop"
with XDG_DESKTOP_DIR="" in ~/.config/user-dirs.dirs, but it didn't help.
I'm pretty sure I locked down the desktop completely in an earlier install, but I can't remember how I did it.