Crime is punished in order to preëmpt the perpetrator and deter others. (Correction is unlikely to be effective and is likely to be a poor value for money; more crimes can be averted by promoting contraception, investing in childcare in poor families and by financing college---instead of army---education for bright poor kids.) Insanity invalidates deterrence, but not preëmption. Retribution is a shorthand for deterrence and preëmption, at best.
Only the perpetrator can be punished, whereas guilt many be spread broadly. If social circumstances necessitate the crime, the perpetrator can be absolved and the society left unpunished but, possibly, redesigned or, at least, altered.
The main argument against capital punishment is its corruption of the executioners: the jury, the judges, the prosecutor, and the public. Whether a convict is better off dead or imprisoned for life, without parole, is unclear, as is unclear which of the options is cheaper, which one yields a fairer trial (the stakes are higher with capital punishment, but the opportunity for revision is greater with life imprisonment), which one will be preferred by the convict, and whether the convict can be trusted to make an informed choice (if yes, the choice must be granted). The third option, Australia, is not what it used to be. Perhaps, it can be replaced by a self-financing prison (a compact kibbutz or a monastery), in order to lift the prisoners' self esteem.
Good life adds, and concludes in death that does not subtract.