A more interesting application would be storing health "meta data" - for example, permissions around viewing health data, or focused data like advanced directives ("code status"). For advanced directives, this could be really valuable to guarantee that disparate health care systems that don't share data are aware of your wishes.
That's just an exercise in signalling at this point, and as far as I'm aware, there aren't many issues with the current implementation of advanced directives. In fact, the few U.S. healthcare systems that implement advanced directive programs are working surprisingly well [1]. Hammer -> nail.
The point is that advanced directives should not be tied to a specific healthcare system. Decentralization (blockchain or otherwise) is an interesting way to make this more accessible.
Practically, advanced directive knowledge requires verbal confirmation with the patient or healthcare proxy; or something like a MOLST (paper).