I don't know about pilots, but you can't become an air traffic controller in the UK if you have any history of mental illness, and particularly depression, anxiety or ADD/ADHD. Odds are that nobody knew what was going on with Lubitz. Reducing the stigma around mental illness would mean more of these people would come forward before stuff like this happens, since they could expect to get paid leave, an psychiatric help, and if they do have to leave their job not worrying about it stopping them from finding a new one. As it is, they can more likely expect to lose their job and have a very hard time finding a new one with that hanging over them. It keeps people from seeking help until things boil over into something like this.
The problem is, it's damn hard to tell who is going to be a danger and who isn't. Granted, you get some who are pretty fucking obvious, but mostly is just 20/20 in hindsight. There are far more people with mental illnesses that there are resources to institutionalise all of them, and you only need to make the wrong call once for something like a mass shooting to happen.
We can't afford to just fire everybody who might be depressed, or hospitalise everybody who might be schizophrenic, and diagnosing there sorts of conditions is just too dependent on people coming forward when something's up. Reducing mental health stigma is going to increase the number of people who come forward when they or a relative are showing signs of severe mental illness.