I don't really think words like 'punish' or 'justice' have any real relevance. It's not about making an example of anyone, it's not about making them right their wrongs, it's not about doing what is considered right by some philosophy; it's simply protecting society by removing a dangerous element and minimising the drain on resources that imprisonment is.
To my mind there are two ways to treat people who are capable and/or willing to disregard a persons basic right to live:
Either we keep a system of incarceration, but instead of feeding, clothing and caring for people for their lifetimes (a logistical and financial drain on society) they should be put to use. Workhouses if you like.
Or they should be culled. Dangerous animals are killed with little hesitation, and they do not have the ability to choose to harm or not. Surely the animal that makes a decision to kill or harm another is more dangerous and conversely more qualifying for destruction?
Maybe I'm just too pragmatic about it all.
so far though any reasonable system (and even that has made errors) costs more than just keeping them locked up forever.
If you want a joke of a system that just kills wrongly convicted people then that's cheap but you're not getting it here.
i guess the most pragmatic way of looking at it would be "rehabilitate", make them useful functioning tax paying crap buying people, the ones we can and lock up the rest for life, doing some job that we don't do in this country any more because it's been sent abroad because it's such low value work, that we could bring back to the country without taking jobs from non criminals.