Point Of Order: Child Support Payments as we know them have nothing to do with the well being of children. The program solely and exclusively exists to save the state money they fear they otherwise would have to spend to subsidize the needs of the child.
By that logic, though, wouldn't unwilling parents have a unilateral opt-out of paying child support in cases where taxpayer money isn't on the line?
I think "shouldn't" is the word you're looking for. And yes, they should have the ability to opt out.