I see your point, in not trying to worsen things for depressed people - but don't you think on a general base, a mentally unstable person is more liklely to disclose something? And when you are really, deeply depressed - you don't care about anything anymore, except if it makes you feel better in that moment.
First, reread everything that you wrote, and substitute "depressed person" for some racial minority. Most of what you have said is still valid and there is a possibility that it is even true. However, you must see that this would be so offensive that your post would be flagged.
Instead of fostering predjudice against people of a racial minority, you are (probably unintentionally) fostering predjudice against people with mental health problems. Do you not see why this is offensive?
Lack of caring for elemental things, including life, is a common trait of depression, not race.
But I did not say, depressed people should not have any clearance. I say, mentally not stable persons can simply not be trusted with every tasks. No generalisation. It depends on the task. So I doubt, you would offer the guarding of the red button for example, a suicidal person. And deep depression, is mostly combined with suicidal thoughts. There was a pilot some years ago, piloting a full plane to join him along his suicide. So much for extreme examples.
And as for the secret new release of the hot new game console x? I don't care about their security. But I see, that companies would want stable persons there, too.