Your son's mental disabilities are not a defense in the sense you are using the term. Guilt or innocence depends on the State's ability to prove the elements of the offenses charged, period. An NGI defense is not a defense in that sense of the word, and only comes into play after a finding of factual guilt. At that point, if it can be established that at the time the offenses were committed he either did not know right from wrong, or was otherwise incapable of conforming his conduct to the requirements of law due to mental disease or defect, he could then be found not guilty by reason of said disease or defect, and committed to the mental health system instead of the criminal justice system. This is not a free pass, just a different form of supervision or confinement. If your son is competent to proceed legally, that choice is his, not yours or the lawyer's. There are many valid reasons a person in your son's shoes could choose to be in the criminal justice system over the mental health system. Hiring a private bar lawyer won't change this legal reality.
It sounds to me your son has been offered a plea agreement he wishes to take advantage of, on the recommendation of his lawyer. If he is factually guilty of more offenses than the State wishes him to plead to, his only viable choices may well be as described, unless he wants to go to trial. Once the other charges are dismissed pursuant to the plea agreement, his exposure on those charges is gone, and his lawyer can argue his mental disabilities as mitigating factors at sentencing on the remaining charge.
Your complaint, as I understand it, goes more to the law than the lawyer, and is therefore for the legislature, not the Judge. There is a reason at least half of the State's prison population has mental health problems, AODA issues, or a dual diagnosis.
This answer is provided for general information only. No legal advice can be given without a consult as to the specifics of the case.
PDs are under a lot of pressure dealing with a lot of cases. If you can afford it, obtain your own attorney. It will cost some money but may well be worthwhile in the long run. Don't let anyone pressure you or your son into anything without fully explaining the options and why they are suggesting that course of action.
The criminal justice system lags behind social science research and cannot cope well with offenders who have disabilities. The Public Defender probably show no interest in the psychological evaluations at the guilt phase because the judge will likely not admit them as evidence until the sentencing phase of the criminal justice process.
This is not intended as legal advice. It is only provided for educational purposes and cannot be relied upon as legal advice. Further no attorney client relationship is or has been formed by answering this question.