CT may be appropriate to further evolve Haskell as a language, but for programming implementations; mathematical categories aren't directly useful. There Haskell is more like any other programming language, just that it's FP.
I'm not debating that; instead, I'm arguing functors are immediately useful in languages like Haskell. Don't know enough about CT to debate that point.
They are. Abstractions like functors makes the language more similar to other structured languages. Otherwise, the same would've needed explicit recursion all over the place, which is more error-prone.