When you wrote "this fictional hash" I read that as talking about the SHA-4 I made up, not the one you did.
I then didn't respond to the rest of the post because when you said "for password hashing, it's a good start" I again assumed you were talking about my hash function, which is not good for hashing. Yours would be perfectly fine.
Apology accepted, and thank you for adding a lot to the discussion further down the page (the interesting maths related to the probability of collisions on a hashed-hash)
I then didn't respond to the rest of the post because when you said "for password hashing, it's a good start" I again assumed you were talking about my hash function, which is not good for hashing. Yours would be perfectly fine.
I apologize.