Yes, the country of Georgia did it. You mentioned a really interesting use case. There's also a pretty interesting use case with the traceability in the supply chain of medication. I work in a few emerging markets, especially West Africa, where you can buy medicine in the drugstore, and the medicine you pick up from the shelves is counterfeit. You could use blockchain technology to trace and make sure that every actor in the supply chain would, for example, sign with their own private key, and that data would be stored on the blockchain.
It's really the public blockchain—for example, the Bitcoin blockchain—that has the most computer power behind it. That's why it's hard to tamper with the data. There are billions of dollars involved if you want to tamper with only one inscription.