Dobbs has not reduced total legal abortions in the USA
By 
Some striking stats here.
The bottom line figure is that there were an average of 5.5% more legal abortions per month in the USA in the first six months of 2023 than there were in the months immediately preceding the Dobbs opinion.
This has been the case despite the fact that legal abortions have fallen to practically zero in 13 states: Alabama, Arkansas, Idaho, Kentucky, Louisiana, Mississippi, Missouri, North Dakota, South Dakota, Tennessee, Texas, West Virginia, and Wisconsin.
What’s clearly happened is that the demand for legal abortion has spilled over from these states to neighboring states. In particular, Florida, Illinois, New Mexico, and North Carolina have seen big increases in their monthly legal abortion rates. I keep using the adjective “legal” because I have no idea if there’s now a significant market for illegal abortions in places like Texas, which recorded around 36,000 legal abortions in the year immediately prior to Dobbs, and essentially none since. The rise in overall abortions in the USA since Dobbs would seem to suggest that no significant illegal market has yet arisen in states that have banned or severely restricted legal abortions, and that instead women are traveling to neighboring states to access abortions services.
It’s always seemed obvious to me that the anti-abortion movement could not possibly be satisfied with Sam Alito’s sanctimonious lectures about federalism and states’ rights, since in America in 2023, transforming abortion into an issue of individual state law would have little effect on the overall abortion rate, although of course it would cause immense harm to certain disfavored classes of women.
The entire logic of the anti-abortion movement requires a federal law banning the procedure, and the Republican party coalition as it’s currently constituted has to be completely committed to such a law, which will become very evident over the course of the next few years, to the extent it isn’t now.