Wow, one thing you are right about. It absolutely is not tied to the enforcement of parental rights because child support is not a parent’s right, it is a child’s right. It has been maintained historically by the courts that a child’s right to support from both parents supercedes an adult’s desire to not be a parent. So your comment about consenting to sex not being the same as consenting to procreation is irrelevant. The right belongs to the child, always. If a child lives with neither parent, they can both be ordered to pay child support.
Custody and visitation are completely separate issues from child support under the law. One cannot be withheld for the other. Nonpayment of support can be cause for contempt regardless of whether or not the payor gets to see the child. The same as violation of court ordered visitation by withholding a child from a parent can be cause for modification of the order and even a change in custody.
But ultimately, none of your arguments are sound. They may have made sense to you but that is because you show very little to no understanding of what you’re talking about.