I think this is a common mistake many Christians make. They think people pay for their sins by spending eternity in hell. But if we are sticking strictly to the transaction model, it would be unfair for someone to pay an eternity of suffering for just a lifetime of sin.
And I expect those Christians would probably point out the common mistake that you are making here, namely, your assumption that the damned cease sinning in hell. I expect they would say something like, "The damned are paying an eternity of suffering for an eternity of sin."
But that's not what I would say. I reject the doctrine of eternal conscious torment, so this is someone else's fight.
Indeed, Jesus did pay for the sins of the whole world.
We both agree that Jesus died for the whole world, sir. Our disagreement is over the hidden premise that it means the whole world "without exception"—that is, every single person—a premise that I do not accept because (a) nobody has provided any good reason to believe that and (b) I am aware of several good reasons to reject it. So much for that premise.
A different hidden premise which I accept, because it is supported by a wealth of scriptures, is that it means the whole world "without discrimination"—that is, both Jew and Gentile, slave and free, king and peasant—for God's sheep are found throughout the world, in every nation, tribe, people, and language (for God does not show favoritism). However, in every case it was for the sheep alone that Christ laid down his life, sheep that are in different pens in all the world. He did not lay down his life for the goats, to whom he will say in the end, "I never knew you."
So, why is there eternal destruction for some people? What is the basis for their verdict? John 3:19 states, "The [basis of the] judgment (indictment, the test by which men are judged, the ground for the sentence) lies in this: the Light has come into the world, and people have loved the darkness rather than and more than the Light, for their works (deeds) were evil."
Proving a doctrine from a single proof-text is a terrible idea. According to the whole testimony of scriptures, the basis for judgment is the holiness of God which lays bare our sin, first by the Word of God but ultimately on that final day. And there are many ways we can describe the condemnation of the wicked but in every case it is sin—including the fact that they hid from the light with a preference for darkness, which is also sin. With flaming fire the Lord will "mete out punishment on those who do not know God and do not obey the gospel of our Lord Jesus" (2 Thess 1:8). And it is predictable that they eschewed light and preferred darkness, for their evil actions were shameful and light exposes it. And light, of course, is a metaphor for righteousness—again, the holiness of God—and darkness is a metaphor for lawlessness, which is sin (1 John 3:4; e.g., 2 Cor 6:14).
But if their wicked deeds, evil thoughts, shameful lusts, love of darkness, and unbelief are all sin, and if Christ fully paid the penalty for all their sin, whose atoning sacrifice removed their sin guilt and satisfied God's just wrath (1 John 2:2), then what are they doing in hell?
... [E]ven born-again Christians can and do commit evil deeds.
We do, and we confess them and repent and are forgiven. That is because God canceled the record of the charges against his sheep who believe, which stood against us and condemned us, taking it away and nailing it to the cross. In other words, those sins were punished on the cross of Christ, whose atoning sacrifice removed our guilt and fully satisfied God's just wrath.
The wicked goats neither confess their sins nor repent or seek forgiveness, because they love their sin and hate God. Their record of indebtedness was not taken away and nailed to the cross, for Christ died for the sheep and they are not his sheep.