I think the study might fail to look at long term trends instead focus on short term ones. In the short term a law will probably fail to change the rate of an activity. However, the long term outcome of many laws is to change how the culture views the activity - which does change the rate.
You’re right, in all these studies, it lacks long term information because we just don’t have that information. But there is a difference between the laws regarding drinking and driving, and abortion. Abortion was not abtainable through legal means for centuries. It came not long after promiscuity of women became a norm. Now, whether we want to admit it or not, it’s part of the culture. It’s just as much part of the culture as promiscuity.
There was never a precedent established for drinking and driving before the laws were made. In addition, one can see in the cars wrapped around street light poles, victim’s body parts strewed all over the road, decapitations via heads going through windshields, innocent (grown) victims affected by the actions of a drunk driver. However, the death of an unborn fetus is more abstract to the general public because one can’t see it. You can try to point it out to people with ultrasounds, etc. You’ll only anger people by showing them dismembered body parts. But one has to admit, the fetus is more abstract than a person standing in front of you. Seldom do I hear of a mother who wants to be pregnant NOT get excited about the ultrasonic picture of her 3 inch fetus. However, those who do not want to be pregnant are not as impressed.
Now, after centuries of men being the only ones allowed to enjoy sexual freedom, women are enjoying it, and seemingly without consequence. Until you change this, there will always be abortion, whether it’s legal or not.
People are not going to risk the ramifications of abolition of abortions, or abolition of birth control. Even in the short term. That would mean they would have to give back what was given to them unconditionally (freedom of sexual expression).
Seriously, I am the only one chaste that I know. I’ve lived in the north, and I’ve lived in the south. It’s the same. Usually people are more “charitable” about my views of living a chaste life. However, I have been called “sick”, “abnormal” and "should be ashamed for not ever having had sex at 30 (when I was 30

) I’ve been called “selfish” as well

Whether or not those who surround me are “loose” or just have one partner (at a time), I am certainly the oddball for practicing chasity. Unless that changes, there will always be abortion and birth control.
That said - the true issue is choice. Woman must know they have a choice for life. They must have safe and viable options for life. Abortionists see no choice, and abortion victims (the mothers), often are violently apposed to accepting there was a choice and they choose death - personal responsibility for murdering their child is something they do not want to accept.
They already know they have a choice for life. They don’t choose it for various reasons. St. Francis and others are right about them having help. However, they don’t feel they have enough help. Some really don’t. I think it’s odd that one woman with a child can be on medicaid for herself, get $400/month on foodstamps, in addition to wic, and another in the same predicament only gets some medicaid for herself and foodstamps. There is a disparity in availability of resources, and a lack of knowledge in how to obatin them, that’s for sure.