@Isaac, I have to agree with you.
The point of our justice system is that a personally affected party cannot be a member of the group that metes out justice, for that would make it revenge. The entire idea of justice is that it MUST be impartial. In our USA system, the few times I've actually served on a jury, the judge polled the jury for their knowledge of the defendant, the events in question, the witnesses, other jurors, and members of the court. In one case, we were even asked if we knew anyone who had been raped, since the case included ra** as one of its charges. Though it is hard to assure, the point was clear. The fairness of the result depends on the fairness of how you get the result.
All too often, people talk about wanting justice when the truth is that they really want revenge. You hear it in the wailing relatives of yet another killing among impoverished neighborhoods. I can understand why there is a Biblical admonition about vengeance. Another Biblical admonition, "let the punishment fit the crime" (though not exactly how the phrase was initially used), depends on there being nothing personal involved in delivering justice. Otherwise "an eye for an eye" quickly becomes "your life for a minor scratch" or something extreme like that. And again, if you let personalities in during sentencing, it becomes vengeance instead of justice.
An oddity regarding justice is that if anyone is sent to prison as a child molester, their time will be a continual Hell because even criminals hate the child molesters. They punish the so-called "short eyes" (to our UK friends, that is prison slang for child molesters) with beatings, stabbings, stompings, and many other types of harsh treatment. I cannot give you overall statistics because they are published state-by-state, but for California, child molesters die in prison at a rate twice that of any other type of prisoner. However, it is usually a case of impartial justice because I guess even totally unrelated prisoners have their standards about whom they allow in their "society."
There was a 1950s movie that was a classic in its day and still has its moments now.
The Day the Earth Stood Still was drawn from a short story "Farewell to the Master" in which a space-faring robot is the judge, jury, and executioner even though a person accompanies the robot to act as its spokesperson. It is relevant to the discussion because in that story, it was revealed that the robots were created to be totally dispassionate, logical, and swift in delivering justice. It was in that sense clearly based on the USA ideal of justice even though we know that errors sometimes occur. There is another discussion or two on this forum relating to emerging AI and how it affects society. How long do you think it would be before we get an AI judge?