That's not quite it. The different legal bases for processing personal data come with different rights; one of them is the right of erasure. It doesn't matter i

That's not quite it. The different legal bases for processing personal data come with different rights; one of them is the right of erasure. It doesn't matter if the data is public or private. This isn't a general bazooka - you'd be unlikely to erase the data that generates a credit score, for example, but then there will be equivalent rights (right to explanation of an automated decision, plus the right to correct a mistaken record). All of these rest on the ability of the subject to gain access to their record in the first place too. Immutability isn't an automatic problem for GDPR - you're allowed to take backups of databases too! - but it is axiomatically more difficult to be in compliance with such an arrangement.