Really the way to fix that isn't enforced ignorance but proper and ironclad severence that says - no donors have no parental rights or responsibilities unless they agree to adopt/marry in later. No matter how convenient it would be to bill the donor instead.
AH yes... the 'punish the poor men' argument. In reality, such laws will lead to powerful men able to abscond their paternal responsibilities by having a good lawyer, while poor men remain indebted to their offspring (as they should be of course).
It isn't about the men or the women. The whole point of an actual sperm or ova donation arrangement is to separate the genetics from the social in having children. Sex and rich or poor it shouldn't matter - the arrangement is specifically to aid fertility - allowing the custodial parents full rights and thus the responsibilities while giving minor compensation to the genetic donor who agrees because the cost is minor to them and they can live an undisrupted life. Without honoring the fundamentals the system breaks down.
The point is proper donors should have no parental responsibilities! It should be impossible to dodge actual relationship support with it or misconduct. Dirty fertility doctors who use their own sperm for all patients? Yeah hit them with 47 counts of child support.
Similarly it would be reasonable to have requirements for eligibility in exchange for the "severance" to ensure the child(ren) will be no more likely to require state support than a similiar couple reproducing directly - changes in circumstances can happen to anyone of course.
