That isn’t really the case. Sha1 still isn’t broken in a particularly useful way. Md5 is still basically safe from pre-image attacks.
Skipjack is the famous counterexample to this: it's been broken up to 31 rounds, but specified usage mandates 32 rounds. Skipjack was given immense scrutiny due to the NSA's role in its design, and we're no closer to a full-round break of it than we were in 1999.
Only seriously lousy cryptographic hash functions would have bad preimage resistance. Heck even the pigeon hole principal makes this aspect of design easier for a hash function. If a wildy used hash function some how had a practical pre image attack i would be more concerned about our process of standardizing algorithms.