It is all a bit of a dilemma isn't it! I'm thinking something I'm finding difficult to put into words here, but I'll, try, and see if you get my drift! Pure fictional scenario but the way, but I think a distinct possibility.
A married woman, married for 3 years, gives birth to a child. Her husband is named as father, but this woman knows that there is a possibility that the father could also be one of two other men that she had a relationship with (unknown to her husband). So we have your "cuckoo in the nest".
Then we have other single mothers who may genuinely not know who the father is! Certainly not unusual! And you might get a woman who just creates a fictional father!
Maybe a simple DNA test to prove or disprove parenthood if a father is named, if it became compulsory, before registration, it may make people be a little more careful - but then the pill was supposed to take care of that one 😄
Surrogacy and donor, if not done openly and legally, could certainly prove to be a whole can of worms!
Don't know if I've actually been able to put my thoughts on it all into words, but as I said, you might get my drift! 😄
Five more replies while I was typing this, I'm not going to try and change it now"