The blockchain is good whenever you need an immutable record. I think the issue that hospitals would face is how to control access to these records. That may have to be second system outside the basic storage system. Many health care professionals need access to your health records and may need to access these records when you're unavailable or unable to give consent.

One technology that would interact well with this is a "Proof of Knowledge" system. This would be useful for a patient to be able to have read-only access to this medical information.