A person's health and any accompanying health issues fall into personal property. It is a person's choice to share what their medical issues are and with whom to share it.
In an age of slyly using the basis of age, education level, and credit standing as a means to disqualify individuals for employment, I am afraid public access to medical issues would just be added as a 'qualifying' item. Here is an example, a good candidate has a fatal cancer but is not yet showing outward signs. With access to medical information, a potential employer may chose to overlook her for a position because of the possibility of having to provide FMLA. She may also be overlooked because of the potential attendance issues and the inevitable loss of an employee due to death.
This person may have 6 - 10 years left to support herself, but would be labeled a huge risk.
Causes of death are part of a death certificate which, like birth and marriage certificates, have always been a matter of public record. In most cases, no harm can be done with the information. In the case of celebrities, the families can endure the judgement of the public if the death was preventable. I don't believe that everyone has a right to know, but even if it was not publicized, they can look it up.