Since this thread was academically oriented for discussion, I'll weigh in with a couple of sub-topics.
1. The eval, like any other part of the test/exam is only valid at the moment it's given. If an ATP passes the flight phys with psych eval on Jan 2nd, his next exam isn't until Jun 30th of that year. A lot can happen in half a year making the test invalid.
2. Standardizing psych exams is very, very hard. Taking into account different psychological profiles which may have issues, however minor and yet be competent to fly, are some of the hardest things in the world to evaluate. It's called the Caine Mutiny problem. Although a person in command may have psychological imperfections, getting an accurate bar on where to draw the incompetent line is not remotely an exact science like saying 'your vision in your right eye has been measured at 20-40, you must wear corrective lenses'. There is limited metric for psychiatric intervention, but there have been improvements over the past 30 years.
3. Most people with depressive events are not continuously psychologically unfit. We call them mood swings for a reason and every human goes through them. How to accurately gauge when a depressive event coincides with a pilots flight schedule? And once you do that, how to determine what depression is mild enough to work through, and what becomes debilitating? Is an airline going to be told it must accommodate a pilot who is suffering from depression enough today that he's off schedule, but they put him back on again when he's chipper? Yikes.
4. If a pilot 'fails' a psych eval, what do you do with them? Vision is correctable with a lens. Are we to fit the pilot with some kind of nutcase metering device? Do we counsel? If so, how do you know when counseling is effective? If there is drug intervention, this opens a whole new can of worms. The Germanwings guy was already medicated. Do we have someone check that he takes his pill every day?
5. Suppose all this comes to pass, and we get a situation where in a fleet of pilots, there are six who are being actively treated for some depression/psych issue. Eventually, by the luck of the draw, two of these six are going to be on a flight together. Does the scheduler have the ability to keep all these six people from flying together? Should they?
There's more, but that should keep the class occupied for a while.