I'm not so sure that Scripture actually supports this. There are many ideas of the atonement. Yes, Jesus died for us. But that doesn't mean that God demands punishment before he can forgive. That's a fairly late theory of the atonement.
I would claim that Jesus' own teachings contradict this. He teaches that God is eager to forgive us. No sign that punishment needed. There are two parables in which people object that God is being unjust in forgiving without satisfying our ideas of justice: the older brother in the prodigal son, and the workers in the vineyard.
I believe several of the prophets said that sacrifice isn't needed. Some people claim it's just sacrifice by hypocrites, but I think Is 66:1-4 seems pretty unqualified. This argument works best if you're not a fundamentalist, since it suggests that some of Leviticus is not God's final word. However even if you think God actually established sacrifice, it's far from clear that it is vicarious punishment. Can you punish grain? I understand sacrifice as a sacrament, a way of making clear the penitent's seriousness about repentance. Remember that sacrifice isn't just for sins. There are also sacrifices to ratify making a covenant.