I read in one of the Taxi books that the Cheers episode 'No Contest' was originally thought up to be an episode of Taxi (with Elaine in Diane's part). The book had detailed notes for the episode. Personally I would have loved to have seen it as a Taxi episode. I can't help but wonder why it was never produced.

Maybe one of the producers didn't like it or felt it needed development. The writer or writers may have put it on the back burner and it never got used on Taxi.

Maybe later, they thought, "Hey, remember that idea we had for Taxi," and re-tooled it for Cheers.

That wouldn't surprise me. Ideas and concepts get recycled all the time.