> Notary services are expensive, and some notaries are corrupt
A blockchain being the place where the act of bureaucracy ends up being stored changes nothing about that.
> OTOH this does seem like a good blockchain application
Exactly. It does at first, because it's about authoritatively storing information, and isn't this what a blockchain is good at? But then you think about how the system actually works and what the requirements are. A blockchain brings you immutable and decentralized storage of peer-validated information. None of these properties are of any value here. We just need a centralized storage that does not forget values by accident, which is basically every other solid information storing system. And most of those are a lot easier to run than a blockchain.