The problem is that it would require everyone to monitor the ledger for falsified versions of their own signature. That works a lot better in the world of Certificate Transparency where Google can scan for google.com registrations. It does not scale well to every human being doing that, or outsourcing it.

The fundamental challenge here is that there's no way to tell, based on a the signature alone, which signatures are "valid" and which are "forged"; they're not cryptographic signatures. And getting cryptographic signatures for lay people is apparently too hard to do, outside of Estonia's digital citizenship initiatives.

It might be neat if the big guys agreed on an OIDC extension that let you piggyback text to be affirmed by the user. Cryptographic proof that jane.doe@gmail.com saw text with hash H at time T and chose "Accept".

Your pointing it out like this should be be obvious, and it is. Yet Blockchain has not become a mainstream use case here.

Like a chain of blocks? Where each block is signed by adding a prefix that produces an increasingly difficult hash?