No, the first question is who is an absent parent. Most beleive Congress extended the class by amendment to include those who are not on welfare. While this is true, it is also true that the extention did not go beyond those who were at risk of going on welfare. If the act is not interpreted with that restriction, it is unconstitutional under South Dakota v. Dole.
This was not argued in POPS. Rather their due process and equal protection claims failed because it did not substantially affect family relationships and the class they contended were adversely affected were not those outside the legitimate reach of the program, but other children within the non-custodial household. These were simply bad arguments that the court did not buy. The court did not establish a new rule of law, or "reclassify" family law to social policy. They suggested the social policy justifying the state law was legitimate because nobody objected to it on that basis. The question was not raised for them to decide.
You're confusing the political rhetoric and the law. Referring to limitations that politicians suggested that were not consistent with the laws they passed would have done nothing to help the P.O.P.S. case. The flaw is in the judgment ... treating non-welfare cases as "social policy" rather than private civil law cases. That's where the elimination of fundamental rights was upheld.