Generalizing map?

A dozen of functions like concat, foldr, mapM, have been generalized through BBP. Then, why do we leave `map` just for lists? Obviously `map` can be generalized, so map :: Functor f => (a -> b) -> f a -> f b map = fmap The current definition of `map` looks too special to be a special case of mapM (map f = runIdentity . mapM (Identity . f)).