I agree with your suggestion. The idea has already made it's way to court and lost :(.

https://en.wikipedia.org/wiki/Dubay_v._Wells

It's actually called a "Paper Abortion" and the scenarios that you describe perfectly represent the concept.

https://en.wikipedia.org/wiki/Paper_abortion

Many women see it as yet another opportunity for men to shirk the responsibilities of fatherhood. I see it like you do: men are more likely to be committed fathers if they have a choice.