Back to the OP original question about why they never played Fool in the Rain live.
If my research is correct, they released ITTOD in August 1979 (at a time when Page & Bonham were both struggling with addictions). Led Zeppelin only played 14 times after that release, starting June 17, 1980 in Dortmund, Germany until their last ever show on July 7 in Berlin.
John Bonham choked to death on his own vomit, a la Hendrix, September 25, 1980 and that was the end of the story.
Listening to Jimmy Page' hi-def remasters series makes it perfectly clear how essential Bonzo was to that band, and it was a heartbreaking end to an amazing group during a time when music trends had not been kind to the original classic-rock juggernauts.
It makes sense to me why Fool in the Rain was never played live.