The thing is that specialist often tend to be very full of themseles. Psychiatry, for example, took a 100-year wrong turn because Freud was too chickenshit to suggest what was obvious, that his typical patients, women suffering from “hysteria”, were actually the victims of childhood sexual molestation. Instead, he made up (deliberately, according to some) the whole Oedipus/Electra/sexual obsession crap and 100 years of pyschiatrists adored him and swallowed it hook line and sinker.
the short answer is, we have no idea what insanity usually is or exactly what causes it. The goal of a jury of randomly selected persons from all over society is to decide whether actions in a particular case fall in the category of “criminal insanity” whatever the local definition. (Usually “unable to distinguish right from wrong”.)
(Aside - IMHO anyone who shows suficient ability to pre-plan their actions, including steps to avoid detection, and possibly hide their actions afterwards - displays knowledge that society disapproves of these actions, and so cannot complain they had no idea they were doing “wrong”. If Hinckley, for example, had the wherewithal to transport a weapon around the USA without having it confiscated at the airport gate, and keep that gun hidden from the Secret Service until he used it, does he really not understand what he is doing is not approved by society? IMHO… )
Besides, a “jury” of experts is a limited pool. Just as both sides can produce their “experts” and get testimony exactly the way they want - a small jury pool is easily subject to becoming commonly known and the “right” people get selected. “Pick Dr. A; he’s known to be soft on abused mothers…” Add jury shopping to judge-shopping. Even for experts, what is or is not legal insanity is a personal opinion and a crapshoot.
And… a jury of experts does not come cheap. If a good psychiatrist can make, let’s pretend, $120,000 a year (sounds low) they are not going to accept $12/day. Do you really want to add $10,000 times 12 for a one-month trial - for no real benefit.