The system does not want the precedent. It can screw up a revenue stream. Plus women voters would really not like that.
If a non-married man can beat having to pay child support if DNA evidence shows he's not the father, then there will be pressure to make DNA matching standard procedure before awarding child support.
And then married men will argue, on "equal protection" grounds, that they should not have to pay child support for children that are the product of a wife's unfaithfulness.
One of my friends shocked me by telling me his new girlfriend wanted to have a baby. He has kids in college. The first thing out of his mouth was “I don’t have any money”.
I’m guessing she has already pulled the goalie on him.