Wrath and mercy are simply incompatible motivations. The first seeks compensation, the latter seeks to do away with payment. The apologist teaches that the plan of Jesus' death was beautiful and perfect, since it allowed God to demonstrate both his mercy towards sinners and his wrath towards sin. But sin itself apart from the sinner simply can't be punished. Further, there would be no point in punishing sin itself even if this were possible.
Sins are just choices or events.
They aren't morally responsible for their effects. It would make no sense at all for God to be wrathful toward sins themselves but not toward sinners, or to have sought the destruction of sins but not those who having committed them are morally responsible for them. Furthermore, God's public punishment of Jesus in effect did punish sinners themselves, because the latter had their noses rubbed in God's fully wrathful reaction to their sin. By showing us just what we deserve for our sins, and just what someone actually underwent for our sake, God makes sinners feel guilty and penitent, which are psychological punishments of devastating force. Standing in the corner amounts to a continuation of the punishment, or perhaps even its culmination.