One minor correction to this (although I agree with you conceptually) is that there are no formal security proofs of the complexity class of hash function attacks for actually-existing hash functions. So there is no guarantee that the most efficient way to break a hash function security property is a generalizable attack on NP problems! It might just be that the specific hash function is weak in a previously unknown way.

A sort-of precedent for that kind of problem which I mentioned in my sibling comment is the correlation weaknesses in RC4. While they're not the most powerful possible break of RC4, by any means, they are unanticipated flaws in the structure of RC4 specifically, and they might well have been discovered by software tools that can't solve NP problems in general. It seems to me that we don't have security proofs for symmetric cryptography at all, including for block cipher security properties as well as hash function security properties, and so while your observation is totally right in general, in any specific case it might just turn out that the cryptographic primitive we were using was weak in an unanticipated way that's specific to that class of functions.

Compare https://en.wikipedia.org/wiki/Random_oracle (although reading that article reminds me of how much I don't understand about this topic)!