In the UK there is already is legal duty placed on Doctors to make a disclosure contrary to the usual duty of absolute confidentiality where the Doctor believes there is a risk of death or serious harm to others.
Pilots already take action against unwanted snooping - unions and CVR disclosure.
Any change to medical confidentiality will probably be met with concealment and avoiding treatment.
WRT Lubitz; if he had been breathing fast or not at all, the papers would have easily wound that into his portrait as a murderer. Likewise if he had had an argument with the waiter in a restaurant last week. Or if he had only lived at home and not had a second apartment 'Oh he still lives at home'. If he had not won that award at the flying school 'He was just an average student'. Or if had no gf 'He was a loner'. Far too much imagination is going on.
Motive / Illness is very unclear. And any response must reflect the actual cause of the crash.