I think a shared, "slow" database could be useful for property deeds. Give the state admin access to override the typical transfer process in case of theft, and then you're left with a 24/7 accessible public database of property deeds, where the current owner and full history of a deed (transfers, liens, easements) can be accessed and verified by any joe with a computer.

It could be useful for professional licenses, too. Everyone could have a verifiable history of someone's professional license - when it was issued, when it was revoked, again mathematically verifiable. You could be sure that someone's record was never changed or deleted without leaving an audit trail.

Though to be fair, the important part of this is the chain of cryptographically signed and timestamped events. It could work without strictly being a blockchain. You could imagine something that behaves more like a git repository with a flat file database in it.