I'm sure this thread is headed towards the end of it's life cycle, just as much as I am sure reincarnation applies to threads. So I am going to summarize my position and my objection to some versions of punishment in the atonement.
The difficulty is the word "punishment". Some contend that Jesus experienced a punishment for sin that was not exactly what we would have experienced. If so, what Jesus suffered was not our punishment in our stead, but a consequence/"punishment" in bearing our sins in our stead. Others hold a simplified version of the Cross where Jesus had to have suffered our punishment (the "second death", Hell, God's hate, a removal of the Spirit, etc). When it comes down to it, most back of the "our punishment" and instead substitute things like "Hell while on the cross", or "because he was God it counted as if it were our punishment". But then we are back at that first option (my position).
Consider Edwards: Jesus suffered the wrath of God for men’s sins in such a way as he was capable of, being an infinitely holy person, who knew that God was not angry with him personally, knew that God did not hate him, but infinitely loved him. The wicked in Hell will suffer the wrath of God, as they will have the sense and knowledge, and sight of God’s infinite displeasure towards them and hatred of them. But this was impossible in Jesus Christ.
Most of the time I believe that Scripture has in mind the physical death and resurrection of Christ (at least I’m sure we can agree this is often the case as Paul bases our hope in the resurrection on Jesus’ physical death and resurrection). But we all suffer a physical death and we all will be resurrected (some to eternal life, others to eternal judgment).
Concerning the Cross, we do not gain adverted punishment insofar as physical death (we will experience a physical death), but life (we will be in the presence of Jesus, and will be bodily resurrected). In this way, the punishment of death (the removal of its “sting”, which was the law) is justly rendered but also conquered in Christ.
This leaves the “second death”, which is a separation as those who are not “in Christ” are cast into Hell, “the lake of fire”, or the “outer darkness”. Jonathan Edwards is right that it was impossible for Jesus to suffer the same punishment that the lost will suffer as the “second death”. It would be impossible for Jesus to experience God’s wrath in the punishment of the lost as Christ’s deity and the Father’s revealed nature prohibits such a punishment. Jesus did not “go to Hell”; was not void of hope, trust and faith in the Father; did not experience God’s anger or hatred towards his nature or his person, etc.
So my argument is that Jesus died in our place, as our representative, bridging the gap that we could never bridge ourselves. Jesus was chastised for our transgressions, bruised for our iniquities, and crushed because it was God’s will to offer him as an atoning sacrifice and lay our iniquities on him. And Jesus lay down his life and bore our sins, obedient to the Father even to the death of a cross. Penal and substitution. BUT the punishment is defined as taking on the consequences of sin, not “our punishment” (i.e., the punishment that we would have experienced) but a far greater consequence because while his earthly ministry was accomplished as the will of the Father by the power of the Spirit, Jesus is still God.