Storing factoids that (1) can't be repudiated by anyone (including the initial reporter), (2) can support attestations in the future (I can prove to anyone that I bought something years ago without showing the thing or making myself known), and (3) can only be deanonymized if and when the user wants it to happen.
1 - Non-repudiation can be done with cryptographic signatures. Storing signed data doesn't require a blockchain. I think the major improvement is related to time-stamping, although there's lots of prior work there.
2 - When would someone ever need to prove this? If you can't prove the "what" or the "who", how is this useful?
3 - For Bitcoin, no, there's lots of tools to de-anonymize users. For others, I think that's true, but what's the use case beyond money laundering?
CA DMV records? Loyalty programs? What's wrong with a database? What's the requirement for decentralized workflows?