Consequences for committing a crime need to qualify as one of these:
* Deterrent. When people see what happens to those who get caught, they are more likely to not commit the offense.
* Punishment. It is a fitting payback for someone who violates the law.
* Public safety. Implementing the consequence will prevent the offender from being a risk to others. It is easy to see why incarceration (or death penalty) would prevent the public from being exposed to the risk of the criminal re-offending.
The deterrent factor makes a nice argument, but the two sides cannot be easily resolved. Many criminals do not learn anything from the negative consequences suffered by others. This is a common feature of the career criminals, and is attributed, at least conceptually, to the antisocial part of the individual’s personality. The addict also fares poorly in learning from others’ consequences. They may observe others die of overdose or get arrested, yet they continue their risky and criminal behavior.
Punishment is a tough subject. Who gets to determine what is ultimately the best form of revenge? In practical terms, this is done by legislatures and courts. But if one is looking for the objective, absolute truth, there is no easy answer. Torah consequences are not exactly punishment either, but are rather, as per the Baalei Kabalah, the appropriate tikun for the neshomoh of the offender. That comes from the Divine Wisdom of HKB”H. Our leaders and dayanim can try to mimic that, but it is mimicry. We may need to follow their psak, but that does not mean it is the absolute truth, except that there is a Torah commandment to follow that.
As for public safety, that seems easy. Putting a criminal in prison means that the public is at lower risk. Death penalty accomplishes that with greater permanence, and with the 2 sides of the issue about death penalty.