Does God not do us an injustice by requiring in His law what we cannot perform?
Not at all. God made humanity capable of keeping His law. But human beings, at the instigation of the devil and through their own wilful disobedience, deprived themselves and all their descendants of those divine gifts.
Scripture references
Will God allow such disobedience and rebellion to go unpunished?
By no means. God is terribly displeased with our original sin as well as the sins we commit, and will punish them in His just judgement both now and eternally, as He has declared: Cursed is everyone who does not continue to do all that is written in the book of the law.
Is God not also merciful?
God is indeed merciful, but also just. His justice therefore requires that sin committed against the highest majesty of God be punished with the greatest penalty: everlasting punishment of body and soul.