Well consider this: the legal system considers time served in prison as forgiveness, meaning that said murderers, rapists etc can go back to the streets once their sentences are over, regardless of whether they feel remorse or whether they are inclined to repeat their offenses. There's also stigma among employers etc against hiring ex-cons, which can help perpetuate vicious cycles.
There are places in europe, for example, where they focus on developing skills so that someone trying to integrate back into society has a more legitimate shot at being successful. Others have implemented non-policing systems such as drug addiction rehab programs, effectively diverting funds from a policy of handling certain types of issues as policing/legal issues and instead treat them as public health issues.
I also recall reading about a small town in US that was composed almost entirely of ex-cons, where they could start a normal-ish life in preparation to jumping back into the regular society, stigmas and all.
The topic of punishment of "lost causes" is itself sometimes a hot button. Some societies consider death penalty acceptable while others do not, for example. There's even differences in laws regarding things like involuntary manslaughter in driving accidents, for example (notoriously, the case of core.js maintainer going to prison for it). We could probably be here all day debating what is "beyond redemption" or not, and not come to an agreement, and we can see from the ratio of small crime inmates that we tend to err on the side of far too much caution / vengeful spirit.
You cannot treat miscreant behavior as if it was a movie, where you beat the bad guy and get a happy ending. Real people are complex beasts and life goes on after the credits roll.