IIRC, that sort of arrangement is or has been done in some jurisdictions. The thought process relating to sentencing looks into the reasons for the sentence - deterrance (might deter an insane person), punihsment (is it truely "punishment" if the insane person can't tell right from wrong?), revenge of society, etc. The defense side of the argument will say that it's unfair to hold a cured person, whose criminal act was taken without knowing it was wrong, beyond the time it takes to establish "cured."
I have a general problem with that, based I think on the ability (and motive) for an actor to fool the doctors. Temporary insanity is another insidious defense.
At any rate, permitting an insanity defense shows a soft side of criminal justice - the challenge is to restrict the defense to those who merit it.
I believe a termporary insanity defense much easier than insane beyond the knowledge of right and wrong.
If I walked into my home and found my husband in bed with another woman, I could easily snap, grab a gun and murder both of them...ie temporary insanity brought on by the circumstances a person finds themselves in.
I do not believe the insanity defense in most cases simply because very few "insane" pleas involve a person who didn't know, or act as though their crimes were wrong or illegal.