The real problem with this sketch of a proposal is the lack of a nice migration plan.
If it is top level and just calls fmap, then the distinction requires random rote memorization of which one you can define.
On the other hand, say you put it in Functor today as an extra member. Currently everybody has definitions in terms of `fmap`, so you'd need to make the two definitions mutual. This would mean enlarging the dictionaries for one of the most common structures in Haskell for a rather far flung removal that breaks everyone.
If we had a way (say a pragma or other syntactic form) to say that fmap and map were somehow the 'same name' or something and so that defining one was the same as defining the other, so that this tax didn't exist, I could see how we might get there.
That sort of "magic" might be useful for making migration plans to get sequenceA to be sequence and mapM and traverse without requiring folks to memorize which one is in the class and which is a top level definition.
Without something like that, I'd remain somewhat inclined against concocting a complicated migration plan to save one letter.