Loads Gingernut
First, confidentiality. My doctor, nurse, physio have been formally trained about patient confidentiality. In many countries they will be inspected in this respect and in the UK they have to be data licensed. If they blabber, their regulator will throw the book at them. Employees in HR will not have this training, will not be inspected, and if they ring up a tabloid there is no regulator to sanction them nor indeed any easy way the individual can obtain compensation.
Second, conflict of interest. The doctor's interest is primarily the patient. Even OH has restrictions on what can be disclosed. HR's responsibility is solely to the company, so if they find the individual may not be able to work so hard or so long, or if they identify the individual may become a financial burden by taking time off or invoking insurance or pension rights the company contributes to, they have a responsibility to inform the company
Third, western countries recognise our medical information is and needs to remain separate to ensure patients have the confidence to be completely open with their doctor. If this practice were widespread, patients will clam up or lie. That effects their health and doctors wouldn't believe their patients further magnifying the issue.
Finally, the likelihood of a complete and open declaration to the insurer falls, increasing the premiums of others and further risking the future of an already commercially precarious product.
Otherwise no issues at all!