You ask, "tell me any other spanking that is REALLY a part of the movie..you can't because THIS is the ONLY one...."
Well, I enjoy "Kiss Me Kate" as much as anyone, but I submit that the entire movie "McLintock," made exactly ten years after KMK, is based on the premise that the shrewish wife is going to get publicly spanked. When it finally happens, it is cathartic, justifying all that has gone before.
And travel back in time a couple more decades, and we see "Public Deb No. 1" (1940), a film which would make absolutely no sense if the socialite played by Brenda Joyce did not receive a public spanking early in the picture. All the picture's rationale is based on that one scene.
There may be others, but these two came to mind immediately when you asked your rhetorical question.