Ugh. Come on, there has been a line of privacy somewhere.
Good luck diagnosing depression when the person being questioned knows it's the difference between his company getting investment or not - here's an e.g. form typical of the assessment you get (in the UK) - http://www.sabp.nhs.uk/Documents/D1.3d2.pdf
How do you think the candidate is going to answer to a question like 'I feel like life is not worth living?' in this situation?
And you didn't respond to my points about marriage, and drug-taking kids. I don't see why they can't be assessed if we permit assessment of mental health as a potential cause of harm to investee/investor.
Perhaps we could look into a candidate's sex life to see if he or his partner are performing satisfactorily? Sexual frustration might take a toll on a startup. Perhaps check to see if there's an ill relative who might die during the life of the startup?
Additionally, I think there's a question of how much you can really assess this stuff.
I knew a person who lost a grandparent + split up with his girlfriend + subsequently failed his degree as a consequence despite a lot of assistance, where I myself experienced considerably worse circumstances with no assistance from the university whatsoever - how would you differentiate between us? Some assessment as to our resilience perhaps?
Not to sound cliched, but this really is a slippery slope situation, even if we could reasonably expect to achieve an accurate assessment.
Education, stigma etc are massive parts of the problem. Being forced to confront it and forcing an industry to confront it head on sounds good to me. When you wait for a depressed person to realize they need help and decide to take action and actually do it you wait too long.
I have no point of reference for marriage and drug-taking kids. I don't know if well adjusted people can leave their problems at home but depressed people cannot, and I do have some experience with that including seeing it take a life.