If Roe were overturned, the issue would return to the states. Several states have already passed provisions for that occasion which would severely limit abortions in their states. Of course, in a state such as New York or California, the state legislatures would do the opposite - they would put no restrictions on abortion. However, I do believe that the abortion rate would at least be cut in half. I also believe that a cultural change would happen in that some irresponsible people would realize that abortion is not a legitimate form of birth control.
Ann Coulter once asked why feminists who love the “pro-choice” label are so against allowing Americans to choose at the ballot box.
I would not bet that way.
BTW, thanks for your succinct explanation of the effects of Roe vs Wade. However, in re Giuliani, claiming "credit" for adoptions and fewer abortions: it's an American political tradition. Office holders get credit for anything good that happens on their watch. Conversely, they get blamed for anything bad. Clinton gets credit for a "robust economy" during his tenure, which was really Bush I's doing. Giuliani can claim credit for anything perceived as good happening while he was mayor, a period now entering "legend" status, i.e. like PT 109, the story gets better with each telling.