How about if they find the actual father, he reimburses the guy as well as pays child support?
I do not see any mention of anyone going after the person whose lie started all this.
Very few women do not know who the father of their child is, and given he was away on war duty at times that the child may have been conceived, she could have said “I am not sure.” But she did not.
How about the state requiring a DNA test as dispositive proof of paternity?
This way, there are no reimbursement issues.
One issue I can see with this is that a mother can indicate you to be the father, requiring the father to submit to a DNA test to establish that fact. Being forced to submit to a DNA test probably violates 4th Amendemnt.
Cost of the test is born by the parent not burdened with the immediate care responsibilities of the child.
If the real sperm donor is found, and has assets, it sounds like there are grounds for a suit for damages. Of course, like this case, only the lawyers win in the end.
The law is full of pre-21st (or even 20th) Century science. In the old days, we didn't have reliable means of paternity testing, and the law falls back on the ancient notions of what to do about it from the days of uncertainty.
What's needed are new laws that reflect modern science. But then, science always moves faster than the law.