Not any of that is true. First I don’t believe that justice exists in the universe without the intervention of humans. Not even Karma is a reality. In fact, it is all a sophisticated construct for revenge. We want people and organizations who have harmed us to pay for that harm and often, we want that harm to either equal or exceed our own pain. This is the way of humans. Even our language supports the concept of revenge as justice: “he must burn in hell for what he has done to my family.” This is language we recognize and condone.
As to the idea of human goodness as a default of thinking and behavior, nothing could be further from the truth. Humans are not innately good as an overwhelming majority, indeed I think we would be lucky to claim that half of humans see good as a virtue. The other half of humans are hard wired for selfishness, cruelty and trickery. They have no interest in other human beings unless those humans can provide for them or profit them in some way.
At the moment that the crime is occurring, is the only time that we can attain justice, for all of the time after that, the only real thing available to us is restitution. If we cannot stop the criminal at the point of robbery or stop the rapist from consummating the rape, then the damage is done and there will never be “justice.” The best that we could ever hope for is to make the criminal give back restitution to the victim. To hope that the perpetrator suffers to match your own suffering is fruitless, as all people suffer and mostly from their own awareness not from someone else’s awareness.
Justice is not something that exists out there in the universe. Justice exists because humans make it so.