I think it's self evident. When abortion is made illegal it's not eliminated it's just made unsafe. People resort to unsafe abortive methods which will result in more dead women along with the fetus. Banning abortion also means that when one does need an abortion for medical reasons, it's difficult or expensive to have one, which will result in fewer women seeking a lifesaving abortion. That America lacks socialized healthcare compounds the problem.
Also it means that someone other than a doctor will be deciding on whether the abortion is medically necessary, and that decision will not be made on the basis of the woman's health (because if it were, the woman and the doctor would be the only ones to make it, and the government and the supreme court would have no say whatsoever). Life and death decisions related to a woman's health that are not grounded purely in actual medicine rather than politics and religion will necessarily result in more deaths (otherwise then I think we should make lawyers and priests into doctors because they are more effective at saving lives).
> the Mississippi law under review in this case does not make abortion illegal until after 15 weeks of pregnancy (and even then there are exceptions like the health of the mother)
I don't think you understand what's happened here. The Mississippi law was written for a world where Roe is still active. This opinion eviscerates Roe. Mississippi has a "trigger law" already on the books for just this occasion, and it will place a total ban on abortion as soon as the opinion is issued. Total abortion bans are going to be a thing very soon, even in the case of rape, even in the case of incest, and yes, even in the case where the health of the woman is threatened. That is all currently on the table.