"Proof" is a legal definition, and legal definitions are defined by the government. Accordingly, I entirely agree that any real property transaction must be tied in some way to the government.

That said, you should take a look at the current system. In many counties, it's still a large ledger of transactions in pencil and paper. In "modernized" counties, but with with extremely restricted access, made intentionally hard-to-access to keep title insurance companies in business.

Title insurance companies charge thousands of dollars on every sale to insure legal claims to property. Any trustworthy publicly accessible database, crypto-based or not, would be a huge improvement over the current system.