So say my use case was birth certificate recording. As far as I understand in the US, there are a bunch of databases run by the states where state employees enter records. There are access controls in place that stop them from removing records. What exactly would "blockchain" solve in this case? And I don't mean theoretical problems.
GDPR doesn't automatically mean right to remove any information. Transactions required for legal reasons, ie money laundering prevention and purchase disputes, can (must) still be kept.
(You can sort of get away with it if it's b2b only or a legal requirement to audit, but that limits the use cases further)