TL; DR I'm not arguing we do these things well. I'm just saying these are the components of justice.
> Not sure what the value of retribution is other than deterrance
It's irrational. But it seems fundamental to human nature. If you remove deterrence, victims and those who identify with them--which in the modern world is increasingly the public--take justice into their own hands.
The 1984 subway shooting acquittal is one example [1]. Goetz shot four people in cold blood. He was obviously guilty. But the jury acquitted, because he was seen as acting justly. (The four kids "allegedly tried to rob him," and there was a lot of unpunished robbery in New York at the time.) The reaction was in excess of self protection. But the public bought into the vengeance narrative because the criminal justice system wasn't doing it for them.
Another example was Chesa Boudin refusing to prosecute someone who unintentionally killed a kid. He said it wouldon't bring the child back. Which is true. But that infuriated the victim's family. They wanted revenge. (They got it through the recall. But most families don't have recourse to the political system to sort things out peacefully.)
> substantial number of inmates commit crimes while in prison
Not on the public. But yes, we fail at this.
> We need to find a better way
I agree. I'm describing tenets of justice. We fail to do justice in America--we do not deter, we do not incapacitate and we certainly don't rehabilitate. We're okay with restitution and retribution, though it's a statistical versus comprehensive approach.
That doesn't undermine the theory, however, which has persisted for millenia and across cultures for good reasons.
[1] https://en.wikipedia.org/wiki/1984_New_York_City_Subway_shoo...