With the ACA, the insurance coverage problem is gone. Pre-existing conditions can't be used as a reason to deny or change insurance rates.
The Fundamentalist problem exists, but seems like much less of an issue with LGBT acceptance being so much better now than it was in the 90s.
I just don't think that health information is so valuable that guarding it like a state secret is warranted. I'm ok with the notion of putting in basic safeguards like not attaching a patient name with the information but I don't see it has horrible if some system can infer absolute identity from that stuff.
After all, seems far more scary that my web browsing generates a far clearer picture of who I am than what you could glean from my medical records.
Having health information public and easy to gather would (potentially) be a significant boon to the study of health information. It would also make it a lot easier for us to make health information sharing systems so you don't have to fill out the same 500 forms every time you go to a different hospital or doctor.