Strong, but self-consciously hopeless, (+1) from me. Existence of the redundant `map` has confused many new people I've worked with. It was based on an early understanding of what was confusing or not to new people. `fmap` can be specialized by an explicit type - you can elide the existence of Functor from learning materials until it's appropriate without having API redundancy. Haskell 1.4 had it right to begin with.
The real argument against this change would the ambiguous type errors that would result. Compile-time type error but easily fixed with an explicit type annotation.
I'm not an imaginative person, but I can't think of any other problems at this time.