Placing vengeance over societal harmony as the end goal of our legal system only has the effect of begetting more vengeance.

Also, your complete dismissal of mental health as a component of crime is suspect and your post is filled with familiar rhetoric. Do you also believe that spanking or otherwise physically abusing a child is preferred for discipline as opposed to other methods? We live in the 21st century and we should take advantage the knowledge accrued, especially from the psycho/neurological fields. Here are some facts to rebut your argument:

Mentally ill people are disproportionately victimized by violent crime. The largest crime-reducing benefit of helping persons with mental illness would be in reducing crimes against the mentally ill.

Some types of severe mental illness increase the risk that a person will perpetrate a violent crime. Risk varies based on many other factors, such as substance abuse, or unemployment. Many of the risks are from secondary effects of the mental illness; for example, cognitive difficulties make employment difficult or impossible.

Many mental illnesses have a genetic component, although the genetic effects are far from fully understood.
Untreated severe mental illness is particularly significant in homicide—the extreme end of the criminal spectrum. Such illness is even more significant for mass murders of strangers.

Treatment of severe mental illness—best accomplished by a combination of therapy and drugs—can greatly reduce violence by and against the mentally ill.

Many mental ill persons who seek treatment do not receive it. Mental hospital beds per capita in the U.S. are lower than they have been since 1850.

Over the last half-century, mental hospital capacity has dwindled, while prison and jail capacity has vastly expanded. Mentally ill prisoners comprise a large fraction of the jail and prison population.

Compared to imprisonment, treating a mentally ill person in a mental hospital is at least two times as expensive, on month-by-month basis. Nevertheless, expanded availability of treatment in mental hospitals could be cost-effective in the long run. Ninety days in a mental hospital might avoid the need for 10 years in prison. Also, we are not including the costs suffered by victims of crime in this calculation.

Greater availability of mental health treatment would provide major savings to society and to crime victims. Besides that, mentally ill persons who receive appropriate aid can be more constructively productive, and helpful to others.

Because many untreated mental illnesses (such as schizophrenia) are degenerative, early treatment is especially helpful. Preventing a first episode of psychosis (loss of contact with reality) can have major lifetime benefits.

In situations where a severely mentally ill person presents a grave danger to other persons, involuntary commitment may be necessary. Due process should be scrupulously protected—such as the right to neutral decision-maker. Involuntary commitment should not require that the danger to others be “imminent.”
Instead of commitment to a mental hospital, “involuntary outpatient commitment” is a less-restrictive alternative for many persons. After hearing the evidence, a judge may order a person to attend therapy and/or to take medication, as a condition of not being committed to a hospital. Such programs have been successful, and should be expanded.