When this subject comes up, I am reminded of past experiences on DDO.
On DDO, people diagnosing others with mental illness was a way to try to take an upper hand in a dispute that had likely gone too far in the first place. This was something that certain people, namely the most mentally unstable (tulle, a/k/a lamerde) attempted to engage in as a way to compensate for the fact that she was the intellectual inferior to most on the site. That said, despite the fact that she held herself out has having some measure of psychological expertise, her conclusions were as unethical as they were inaccurate. Of course I, too, partook in that activity when I was a bit younger and more prone towards sanctimony, and by no means is my criticism of tulle/lamerde meant to exclude myself from historical engagement in that particular type of mischief. It certainly is not. On all counts it would be inaccurate to say that anything of that sort was "good" for the site, the conversations (read: heated disagreements) we were having, or anything else.
But on the other hand, insofar as no one here (except maybe myself and a few other people, who I'm sure know who they are) have anything resembling expertise in the field of psychology or psychiatry. Further, of those who do have some expertise, it's not from having been a shrink so much as it is from having had to utilize principals from psychology in our jobs to accomplish specific tasks. This may give some the ability to navigate some of the more nuanced complexities of human interaction, but little more. In this way, even a "diagnosis" from the most sophisticated person here can easily be written off as "banter" at worst. So, there isn't much harm in allowing this species of mischief to go on so long as proper context is provided -- as it obviously will be ("you're not a shrink!"), for the obvious reasons ("and therefore you don't know what you're talking about! blah blah blah!").
