In Pilgrim's Progress there is a place where Jesus himself makes the guys lie down and he flogs them. And no, I don't think divine justice is the point of that. Same if your child talks back. We know we live in a physical world and we understand that, as sophisticated as we think of ourselves to be, we still live under a system of rewards and punishments, some natural consequences, and some administered by whatever authority we are under.
But am I to understand that you don't agree that a person who offends at one point of the law is a law breaker as in James 2:10 and may have judgement without mercy. Or as in Hebrews 2:2 "every transgression and disobedience received a just recompense and reward". Or, when we are told to withhold righting wrongs done to ourselves and to defer revenge because God claims that for his own and will do so himself?
An example of a child that sasses you is not exactly what I had in mind. Even more to the point would be just to take a quick read of Jude where the judgement of finally impenitent folks is described. In those cases your no. 4 above could be said to apply, to the extent that righteousness and holiness are upheld in the punitive judgement of the wicked. But these passages show God punishing with a final declaration based on sin unforgiven and unrepented of with no goal but that the punishment be done - because it is God's decision that it should be so.
And I think where you are mistaken is that there then are areas where punishment functions with no beneficial healing or fixing of anyone and is not like punishment on a sassy child which is more accurately called discipline. In Jude, in Hebrews where they have neglected the final act of God towards us in sending Jesus as a sacrifice, in wrongs to saints that have not been repented of - those would be cases where the punishment functions only to satisfy the justice of God and thus to "make things right". I don't see why this should be difficult to understand.
I'm not saying everyone who claims to be a Christian nowadays believes this. I think there are many who don't believe God will truly punish anyone, I guess because they figure we all had it pretty tough here and let's let bygones be bygones. Wasn't that Rob Bell's philosophy.
I do not know Rob Bell's philosophy. I also have not read John Bunyan in decades. I merely pointed out what God said about His justice.
Justice is justice. If a child murderer is sentenced to death the punishment has a purpose (to remove that element from society). It is not punishment to satisfy justice, but punishment to bring about justice by removing the unjust.
You are wrong. Punishment is not a means unto itself (not what satisfies justice). There are no passages that describe justice on those grounds.
Had you continued to read Jude you would find that the punishment was to remove the ungodly (they cannot stand in the presence of God's glory).
Had you read the Old Testament you would have known this because God Himself said that this punishment is to "remove evil".
You have a bizarre philosophy for today. You repeat 16th century humanism as if it has not been shown repeatedly to be unjust, ascribing that unjustness to God.
Rather than reaching back three and a half centuries why not just read the Bible and believe God's words?
God told you the purpose of temporal punishment (bring repentance, deterrence, and instruction). God told you the purpose of the final judgment (cast out the wicked, remove evil, no wickedness will exist).
God told you that He is just. God told you it is unjust to punish the Innocent, to punish the Just, and to clear the guilty. God told you His words stand, He is faithful, He does not change.
Yet for some reason you ignore all of that to lean on the secular philosophy you quote almost verbatim.
How do you define justice?
Do you draw on secular humanism (justice is the punishment of crimes to satisfy the law; the role of a judge is to avenge the law by punishing crimes")? Or are you willing to listen to God (punishing the innocent and clearing the guilty are both abominations to God; it is wrong to punish the Just)?
I agree the Law had punishments for offenses. BUT punishment did not satisfy justice (there was an important reason for the punishment, God told you the reason). And the Law, while certainly just, was NOT justice itself (it was one manifestation, and it served to show us we fail to meet God's justice).
What you are rejecting is more than those passages.