True - I suppose the hash function just ends up being the convolution of say an interior CRC and some exterior hash function. That gives us low to zero chance of something mathematically provable. But perhaps some arrangement of functions forces an attacker to scramble the inputs in more drastic ways such that the original data must be altered by more than a handful bytes it could perhaps raise the difficulty on a practical basis.
But to make a strong cryptographic hash, you don't want predictability based on inputs. If you end up with some kind of pattern where getting the same output values requires modifying huge ranges of bytes, that lets attackers reason about inputs that generated a hash.
