Actually, I'm all for it. The child may one day wish to know the name of his/her father. With the strides in medicine being what they are, it might one day serve the child to be readily able to have access to his/her father's medical records in order to treat some disease or other medical problem that pops it ugly head. I can't see any logical reason for not listing the father's identity.
I will agree that it's more beneficial to the child to know their family history. But there are several problems with what you are saying.
1 - Nobody has access to another person's medical records, unless specifically granted. I know who my father is. I know his full name. I know what his full name at birth was, and I know what it was changed to and when it was changed. But I have no access to his medical records. That he is my father does not give me access. That I might have an important reason for wanting access does not give me access. Privacy laws prohibit me from having access, unless he grants me permission.
2 - There are instances when a woman does not know who the father is. Your moral qualms about her sexual behavior aside, this is a perfectly
logical reason to not list a father.
3 - Regardless of whether the mother's decision is logical or not, the child is the one who ends up paying the highest price. The child is an American citizen, but will be denied the opportunity to produce the kinds of records that are typically relied upon to prove that citizenship.