Catholics: How is it possible that an afterlife cleansing through punishment is necessary if...?

Purgatory is part of Christ's cleansing of our sins. Without the death of Christ on the cross, Purgatory would not be possible. It is only by His grace that we can be cleansed of those remnants of sin that remain in us at the moment of death. The Proterstant heresy that Christ "covers over our sins" and somehow smuggles us into heaven "like dung hills covered with snow" (words of Martin Luther) is not compatible with true Christianity. God in fact cleanses us so we actually ARE completely pure when we enter heaven, for the bible tells us "nothing unclean can come into God's presence".