One problem with this strategy is that such evaluations are relatively subjective. Like everything else in government, the process would become stacked with politically motivated individuals that have an agenda, and the judiciary would ultimately be biased according to their whims.
Oh definitely. My offhand idea would be to do a sort of jury selection. Pick 20 random psychiatrists from the AMA roster, let each side remove 5, and have the remaining 10 submit evaluations. I think if a majority (so 6) find them incompetent to be a judge, there should be some form of citizens voting on whether to keep them or not. Not state legislators, but actual citizens.