Anonymity in Blockchain is good but can also be used for illegal purpose or fraud. Another disadvantages of Blockchain is when private key is lost, that means one has no access to the account again and there is no way to retrived it, this has happened to me before and it was so painful.

Implementation of Blockchain in health sector is good as you have said, but to me doctor giving an appointment in a month to check your health status is not a bad idea. No doctor is born a doctor, they only learn with their experience in school and field. All the doctor want to know and record is the prognosis of the illness with the drug they prescribed, whether or not the treatment work.