Cryptographically secure hash functions are irreversible so that ciphertexts can't be decrypted by running the function in reverse. But none of the data in a block is secret, so the block hash is just a checksum, and shouldn't need to be cryptographically secure. Am I wrong?
If someone find SHA256 pre-images, i.e. given y, find an x with SHA256(x)=y, in time 2^240, i.e. 2^16 times faster than brute force, then SHA256 would be considered broken.
But such an attack need not have any bearing on the cost of bitcoin mining.
The latter corresponds to find *partial* preimages.
As long as finding a preimage to n leading 0s takes time roughly 2^n, then bitcoin mining is safe.