I think a system like that is a great idea, I'm just not sure how a blockchain helps. The things that make a blockchain interesting (uncensorable, immutable etc) aren't that important here, and with a public blockchain you still need a whole separate system that's doing access checking (maybe your doctor has a key that decrypts the onchain data). To me that system of sharing data with providers, and giving them credentials to access the data is the difficult part, and blockchain doesn't help.