I've worked at places that would disallow re-use for the last 30 passwords. When you're forced to change every 3 months you're looking at a company maintaining a password history for over 7 years.

How is that managed? Are they hashed or stored in the clear? If they were hashed, then they would have to know which algo to use for a password at a point in time otherwise they would lose that data whenever they switched the hashing mechanism.

And when that data inevitably leaks, attackers have a nice table of passwords and metadata that will easily help them out in other places.

A solved problem with public key crypto, where you are in full control of the secret and can take your own steps to protect that.