But would that allow me to conveniently omit any negative info from future credit applications? The banks would quickly start sharing this info with one another and become de facto CRAs themselves.
I don't understand why they're proposed as a solution to this type of problem at all. I'm a big fan of blockchains, I work for a company/project completely reliant on them, but I don't get where people think they'll be useful for things like credit monitor and health care records. It makes no sense to me.
Just to play devil's advocate, since I don't think they are a good solution either. Unlike healthcare I think you could use some of the properties of a blockchain to help reduce the risk of leaking personal information during credit checks. For example: you could prove your identity by making a transaction and then show a timely series of past payments.
(If you're not laughing then you need to admit you have a problem)