I think it starts to make sense if you can hold your data and only it share it using hashes of that data without exposing it. For example, I could hold the private key to my DNA, where each strand would be hashed allowing me to share portions of my DNA data with companies without sharing the entire thing. And it makes sense to do that over a public ledger.

But the hash of health data isn't informative. It doesn't make sense for a doctor to view, for example, the hash of a blood test result. They need to see the actual result, not its hash. The same thing is true of DNA sequencing results. The only thing I could learn from the hash of a DNA sequence is that it's different from one I have in a database. But I need to know exactly how it is different -- precisely the clear text content of the sequence -- for that to be useful information for a patient or for research.

> And it makes sense to do that over a public ledger.

Why? It makes much more sense to keep the data to yourself, I do not see any advantage in making it public and intermingling it with data about other people.