Why not just forgive the sin? Even if you must punish Adam and Eve why punish the children that havent been born yet?
Christians don't fixate on Adam in the same way, that is a JW thing.
Adam was more like a representative of humanity. The focus in the gospel is on our personal responsibility for our actual sinful actions. For those we deserve death but the price has been paid on our behalf by Jesus.
The idea of vicarious punishment is crucial - pun intended. It was central to the Jewish sacrificial system where the blood - representing the life - of sheep and goats stood in place of the lives of sinful Hebrews. Jesus became the "Lamb of god that takes away the sin of the world".
The gospel as preached by the early church was about a restoring of relationship between god and the penitent sinner in the present life. It was about spiritual restoration as opposed to the JW gospel which is materialistic in nature.
Disclaimer - I am not defending this idea as either rational or moral.