Going back to the traditional teachings of the Church Fathers, it can be seen that when the specific mention of the death penalty is raised, it is always conditional upon it’s role in the safety of the community and is unfortunatey being skewed by the practice of isolating its mention from the whole context in which it is referred to.
This is not, at all, true, beginning with Genesis 9:6.
Even the Catechism establishes that the primary purpose of sanction is to redress the disorder.
The Catechism states: “The primary scope of the penalty is to redress the disorder caused by the offense.” 2266 This is a specific reference to justice, just retribution, just deserts and the like, all of which redress the disorder.
Primary, meaning everything else is of lesser value.
We must first recognize the guilt/sin/crime of the aggressor and hold them accountable for that crime/sin/disorder by way of penalty, meaning the penalty should be just and appropriate for the sin/crime/disorder and should represent justice, retributive justice, just deserts and their like which “redress the disorder caused by the offence” or to correct an imbalance, as defined within the example “If anyone sheds the blood of man, by man shall his blood be shed.” “This teaching remains necessary for all time.”
To “redress the disorder” has various relevant meanings – to make amends, to correct the imbalance, to set right, to remedy or to rectify, even reform, all of which may be used in the context of justice, just retribution or just deserts (and similar concepts), all of which have relevance in the context of the religious.
When it comes to reform, the second sentence is important:
2266: “When (the offender’s) punishment is voluntarily accepted by the offender, it takes on the value of expiation.”
The reformation and correction of the offender is a hoped for, even expected, component of justice or just deserts.
However, unlike the imposition of justice or retribution, which is mandatory, the reformation and/or moral correction of the offender will be voluntarily accepted or rejected by the offender, as a consequence of free will.
Retributive justice, just deserts and the like must be imposed. The correction or reform of the offender will be accepted or rejected by the offender.
The Catechism agrees, with:
2266 ending " . . . Moreover, punishment, in addition to preserving public order and the safety of persons, has a medicinal scope: as far as possible it should contribute to the correction of the offender."
" . . . as far as possible . . . " concedes that this is a sometimes proposition.
It is the same with God and his flock, as it is with parent and child. When a parent sanctions or punishes their child, they hope and often expect that such will bring about reflection, reform, redress and correction and, often, it does. It is a foundational to sanction.
Therefore, the foundation must be that we impose sanction based upon the evidence that the offender is guilty of the wrongdoing and because of that wrongdoing, we impose sanction, based upon justice (and its many similar considerations) and because of that justice, we reap the benefits of that justice, which include the protection of society and many other benefits, inclusive of the hope and expectation that some offenders will seek reform/redemption/correction, as a reflection in sanction and a product of grace.
A crucial element of that justice, which is reformation/correction of the offender, will always remain, a hoped for, but voluntary expression of free will by the offender, which may also provide, the immense value of expiation, when the punishment is “voluntarily accepted” (2266) by the offender.
Voluntary acceptance has four components. The offender/aggressor is guilty of the offense, the aggressor pleads guilty to the offense, the aggressor accepts the sanction imposed and the aggressor does not appeal the sanction imposed. Anything short of that appears to negate voluntary acceptance.
Expiation, a product of God’s grace, will be seized upon or rejected by the offender, based upon their own free will. It is arguable, as per Aquinas and Augustine, that the death penalty is better apt to provide that correction and is, therefore, more in tune with the eternal aspects of the wrongdoers salvation (see paragraphs/references 3 and 4 within Reference 2 and also 5, below).
Romano Amerio: “The most irreligious aspect of this argument against capital punishment is that it denies its expiatory value which, from a religious point of view, is of the highest importance because it can include a final consent to give up the greatest of all worldly goods.”
"This fits exactly with St. Thomas’s opinion that as well as canceling out any debt that the criminal owes to civil society, capital punishment can cancel all punishment due in the life to come. His thought is . . . Summa, ‘Even death inflicted as a punishment for crimes takes away the whole punishment due for those crimes in the next life, or a least part of that punishment, according to the quantities of guilt, resignation and contrition; but a natural death does not.’ " (Paragraph 3, Reference 2)
All we can do is hope and, in some cases, expect, that beneficial reformation will be sought by the wrongdoer, although we cannot force it upon them. And, in this religious context, such reformation will result in expiation and redemption, through the grace of God.