Well there is little evidence that the experts you're alluding to will be correct in that assessment, quite to the contrary.
https://www.nbcnews.com/health/heal...n-when-countries-make-it-legal-report-n858476
https://www.nbcnews.com/think/opini...p-when-procedure-outlawed-it-does-ncna1235174
https://www.hsph.harvard.edu/news/features/abortion-restrictions-health-implications/
I listened to a podcast over the weekend and the guest was an abortion services provider located in Texas. She tracks the service trends she sees and since the Texas heartbeat law went into effect last September, she's experienced a considerable increase in demand for abortion services. Granted, it's one provider in one state, but all of the women in Texas now are operating under a very tight legal time frame and because of that additional pressure many are opting for an abortion vs. keeping the child because many women consider it a much easier thing to reconcile the regret of going through with an abortion than bringing an unwanted/unintended child into their families.
Conservatives should know by now that providing access to birth control at little to no cost, having free access to family planning services and prenatal health care, sex and behavioral education for our kids in schools are factors that will actually lower abortion rates nationwide. Instead, conservatives insist on approaching the perceived problem by limiting certain human rights and liberties because they think they have the moral high ground on the issue because they believe they know what their sky god wants them to do. Their approach will cause more suffering, death, abortions and unwanted kids stuffed into the system. That tells me all I need to know about their motives, and it doesn't include lowering abortion numbers at all, it's all about control.
State governments would be wise to tread very lightly or not at all on this long standing right of women. I believe the blowback from any radical moves by the States will be substantial.