But it is not general 'sins' that Jesus was supposed to die for - it was Adam and Eve's original sin that everyone inherited. This was supposed to be a cosmic balancing.
“So then as through one transgression there resulted condemnation to all men, even so through one act of righteousness there resulted justification of life to all men. For as through the one man’s disobedience the many were made sinners, even so through the obedience of the One the many will be made righteous” (Rom. 5:18-19)
I always thought this was the fundamental value of Jesus sacrifice - making up for Adam's sin. The Apostle Paul was quite explicit on that point. I suppose I can see how individial Christians might fudge an argument that this was generic human sin that Jesus was supposed to redeem but that is to ignore a central argument that Paul was making about the meaning of Jesus sacrifice.
For it was Adam who was first created, and then Eve. And it was not Adam who was deceived, but the woman being deceived, fell into transgression” (1 Tim. 2:13-14)
For since by a man came death, by a man also came the resurrection of the dead. For as in Adam all die, so also in Christ all will be made alive” (1 Cor. 15:21-22)