You have a point. Another advantage is, all that state other than the secret phrase is insufficient to derive the password, and could be passed around insecure

You have a point. Another advantage is, all that state other than the secret phrase is insufficient to derive the password, and could be passed around insecurely, while the secret phrase could be memorized. But I suppose one might achieve the same thing with a GPG-encrypted file of randomly generated passwords. Still, if you lose all relevant files, you should be able to reconstruct the hashing scheme and recreate all passwords that didn't require state. Whether this matters is up to the reader.