Hi wildermuthn! Welcome to the board.
In response to your question, you have to remember that hell is not the beginning of life for those who are in hell. Rather, it appears to be the place where rebels and rejectors-of-God-in-this-life go after a judgment/separation by God based on their actions in this life. If all those folks ever knew was suffering, I think you’d have a point that there’s no hope for them, because suffering itself does not lead to life. But everyone experiences at least a little grace in this life, and then for sure everyone comes face-to-face with the King of kings at the judgment–so at least at the judgment, the mercy and love of God begins to dawn on us all, regardless of what we’ve experienced in this life. I think it also becomes clear to those who are in hell that they are there reaping the consequences of their actions in this life, so they’re more and more aware that the cycle of violence perpetrated on and by them in this life is completely hopeless and futile. Therefore, they (gradually?) come to realize that the only way to life is by accepting the mercy of God offered through the work of Christ. Jesus ends the cycle of suffering/violence for all, and as soon as they trust him and his work they experience deliverance from that cycle.
So it’s not that the sufferings of hell automatically make people better–“purify people of their sins” is not a UR claim, but a Catholic one it seems to me. Rather, the sufferings reveal that there is no other way to life and happiness than trusting in the work of Jesus, which ends all sin and death (suffering) forever. It seems to me that the length of time people spend in hell is directly related to how long it takes them to realize that perpetrating the cycle of violence only leads to more death, and the only way out is repentance and turning in faith to the only true Source of life, Jesus.
To refer to your story, people in hell come to realize that God has “lit” their “lamp,” either by remembering something they learned in this life, or by understanding some truth revealed at Judgment Day. The sufferings of hell clearly show that the only “lamp” is faith in Christ, and everything else is utter darkness and death.
Hope that makes sense.