For most of my life I've felt that you have to have some kind of psychological defect to want to be president. But since we need a president anyway I figure we just have to make do with the situation as it is. Hell, maybe it's the defect that makes it possible to do the job.
Anyway, we've never needed a psych eval before. Asking for one now is special pleading, as far as I'm concerned.
He's had the same evaluation as every other president: the evaluation of the American people. And a majority of Americans in a majority of states have evaluated him as being fit for office. It's true that a majority of Americans living in a few of the densest urban centers evaluated him as unfit, but I've always felt that you have to have some kind of psychological defect to live in a dense urban center. So there's that.