If, when all is finalised, it turns out that the accident was caused by a seriously mentally ill man hiding his condition from his employers because he feared for his career our industry will need to enable doctors to directly report serious concerns.
Thats not going to help I'm afraid:
1. Mandatory reporting may prevent people seeking medical attention. Different jurisdictions have different approaches to the issue of patients with epilepsy driving. Some authorities favour mandatory disclosure to the licensing body, but there is evidence this prevents epileptic patients declaring their illness and obtaining medication.
2. There is mandatory reporting for a few specific issues such as child abuse. Sadly most children killed by their parents are well known to the authorities. Often a "child at risk" is reported multiple times (by doctors, teachers, police etc) during the last few weeks or months of life. The problem isn't notification, but rather effective intervention.
3. A pilot seeing a doctor for depression or other mental illness will likely declare another occupation if there was mandatory disclosure. Absolutely guarantee this happens already out of concern of disclosure.
This issue of mental illness doesn't have a simple solution. Mental illness is common, but only a tiny proportion of people affected by mental illness will do anything like this. There are no tests that can predict if someone is high risk. Routine psychological screening can be employed, but intelligent people with insight can easily "spoof" the test. "Do you ever have feelings of hopelessness.' Umm, think I better say "No' for that.
A more effective measure would be being rostered with the same (or a few) colleagues. If you get to know someone, you will be more likely to pick up a change. Ongoing observation by a colleague over weeks and months will beat a 10 minute screening assessment. Small specialist military units will often spot when one of the team is not right. Larger military units much less so. However I am sure this rostering presents almost insurmountable logistic challenges to the airline.