I had my modern conceptions of fairness blown far, far away

So I'm perusing - no, strike that, try break-neck speed reading - Augustine's City of God, and I come across a quotation of Genesis 17:13-14:

[God spoke to Abraham] "He who is born in your house and he who is bought with your money must be circumcised, and My covenant shall be in your flesh for an everlasting covenant. And the uncircumcised male child, who is not circumcised in the flesh of his foreskin, that person shall be cut off from his people; he has broken My covenant."

Let's get this straight: a baby boy who is not circumcised by his parents has already broken the covenant with God. If he dies at nine days old and has not been circumcised, he dies outside the covenant of grace. Whoa.
Then Christ comes and renews the covenant, replacing circumcision with baptism. But does this change the principle? Obviously there is enough condemnation in original sin to damn a babe in arms. Again, the burden must be on the parents.