Earlier I described some consequences of abortion prohibition.
Probably the most significant effect of such a policy would be to safeguard female sexual virtue. It should come as part of a package that would strengthen the family, including (1) making marriage more attractive to men by improving their legal standing including as regards their children, and (2) making divorce more difficult for women to initiate.
In short, the main aim of the prohibition will be to raise the costs of promiscuity and premarital sex to women, not to "save lives." This is because ideally, the children who under liberty are aborted will under prohibition never be conceived in the first place, as women, facing the new incentives, abstain from whoring themselves.
It may be true that young women eager to jump into any guy's bed are "stupid," but then so are criminals, but that does not mean there is no deterrence effect of the threats of punishment. Some of this effect will consist in greater parental guidance for young women, so the girls' "stupidity" is counteracted by greater parental strictness toward them.
The upshot is to make women somewhat more chaste and hence better marriage partners rather than the semi-prostitutes who have ruined their own capacity to fall in love. No man really wants to have a wedding where the bride has slept with most of the guests.
The obvious cost of the prohibition is the suffering of the women who still have abortions and are caught and punished. In addition, the situation resembles the drug war in that even though, unlike drugs, there is a victim, the fetus; like drugs, the victim will not complain. Disrupting the "mutually beneficial" in the narrow economic sense illegal abortions between the women and "doctors" will be a serious pain to society. (For example, society will still further become infested with spies, rats, and informers; police corruption will assuredly rise; some women are bound to die or be physically harmed from incompetently performed black market abortions; and so on.) If there is empirically much defiance of the law, punishments will have to be ratcheted up, and I am not sure juries will be prepared to send a woman to prison for 15 years for an abortion.