Why Can't Reverse Hashing Prove $P \neq NP$?
Give a polynomial time hash function that takes exponential time to compute the inverse of.


That’s an open problem. It can’t currently be used to resolve $P$ vs $NP$ because no one knows if there is an example of such a function. In CS, we often assume that $P\neq NP$ and that there are cryptographically secure hashes, but that’s an (experienced based) assumption, not a probable fact.