Well I suppose a Mother could put "Unknown" - if the Father was actually unknown. Putting down "Unknown" when it isn't true, and then signing the form would actually otherwise be known as Giving False Statements and Defrauding The Government.
I think we are simply going to have to agree to disagree here. You seem to be of the opinion that I (and some others) are advocates of forcing undesirable parents into the equation all in the sake of saving tax dollars.
I on the other hand firmly believe that the taxpayers aren't forcing the issue at all. The taxpayers have nothing to do with choosing the parents of a child. That choice is made by the people who create the child and the consequences of those choices should then be born by the people create the children.
There are of course cases where parental rights should be removed. However I can't ever imagine such a scenario where one parent should have the right to unilaterally deny another parent his rights and obligations and then turn around and request the public to pay in his place. If somebody is an unfit parent, then follow the court process and prove he is an unfit parent and that your child will be damaged by having contact. Simply saying "Well I think it'd be better if I didn't have to fill out that paperwork and follow the law --- all for the sake of my child. So just give me the money." just doesn't cut it for me.