This reminds me of something Larry Page said at TED this year: I say, wouldn't it be amazing if everyone's medical records were available anonymously to research doctors? And when someone accesses your medical record, a research doctor, they could see, you could see which doctor accessed it and why, and you could maybe learn about what conditions you have. I think if we just did that, we'd save 100,000 lives this yea…
As for medical records, no institution hoarding them has any interest in sharing them. Patients are not consulted on this, so their privacy is only a tiny part of the reason. As far as patient privacy goes, “anonymising” them is not so easy either, as another commenter already explained.