I will simply say two things.

First, even accepting your view as correct, the proposal is not abortion up to the point of birth. The State is allowed to regulated (prohibit abortion) and there is an exception for the mothers physical and mental health. I am quite confident the state would have the right to enforce regulations about those exceptions.

Second, you appear to hold medical professionals and pregnant women in very low regard if you believe they will terminate a pregnancy up to the point of birth because they are stressed out.