That doesn't work under the laws we have. Here's the counter argument which always prevails. It's not the child's fault. The interest of the child comes first. This means that a mother can't bargain away child support because it's not hers to bargain.
The way out of this is for the child support to be paid by the state but then again, what did taxpayers do wrong?
Alternatively, since the boy was a child when he's victimized this dispute comes down to one child's interest versus another child's interests, and you shouldn't punish one to uphold the rights of the other. A child doesn't have a right to child support from a dead parent, so that child is just out of luck and the same here, this is out of luck.
Just as a heads up, child support is
not going to be paid by the state, period. That doesn't happen, what does happen though, is that the state takes a vested interest in finding the non custodial parent and charging them child support if the custodial parent goes on state assistance. They also demand that the father assist in paying for the labor and birth costs that used assistance funds. Which is what appears to be happening in this case.
That said, yes, if the mother is on welfare or any state assistance, ultimately the taxpayers end up paying for it.