Women running for the presidency or holding any elected political office or any sort ---city, state,local --- had exceedingly little to do with the legalization of criminal abortion. Ironically and peculiarly enough, the emergence of abortion as a broad-based "popular" "women's" political issue happened after abortion was legalized via Roe vs Wade.
As I mentioned, groups like the National Organization for Women did not take up abortion in the late 60's --- which really frustrated the male abortion vanguard like Nathanson, Lader,and Baird.
NOW's focus was, locally, anti-discrimination workplace issues and challenging men-only social spaces, and nationally, the ERA. They actually churned out a ton of propaganda refuting the idea that there was an abortion-ERA connection. They felt that any link to abortion would be toxic to the ERA, and assailed conservative lawyers (like Phyllis Schlafly) who insisted that the ERA would be used to buttress a "right" to abortion and to abortion funding.
Pro-abort radical left feminist lawyers (like Sarah Weddington and the equally odious Margie Pitts Hames) got their support from the ACLU and the Georgia Legal Aid Society.
After legislative successes for abortion in CA, NT, HI and other liberal bastions, their political /legislative campaigns were losing steam or stalling out altogether. Abortion was not a popular political issue. That's why they preferred getting things "fixed" in the courts rather than the state legislatures.
Now, of course, abortion is "the" litmus test and rallying cry for ambitious female politicians and their associated demented maenads and pussyhats. But it was not always so.
Further writing....”Most scholarship on abortion has focused on two moments of legal change:. when abortion was ‘criminalized’ in the mid-19th century..... and when it was ‘decriminalized’ a hundred years later in the mid-1960s and early 1970s..... The century of illegal abortion is typically treated as obscure and unchanging. I find, however, that the history of illegal abortion was dynamic, not static.”
Analysis of public policy should examine how policy has been implemented and by whom, rather than be narrowly restricted to federal legislation or agency activity as much of the regulation of abortion was carried out not by government agents, but by voluntary agencies and individuals. .....as an example...........It would have been virtually impossible for the state to enforce the criminal abortion laws without the cooperation of physicians. State officials won medical cooperation in suppressing abortion by threatening doctors and medical institutions with prosecution or scandal ....
By the 1940s and 1950s, physicians and hospitals had become so accustomed to this regulatory stance toward women and abortion that they instituted new regulations to observe and curb the practice of abortion in the hospital. The medical profession and its institutions acted as an arm of the state
Her book brings attention on the nature of the public sphere, its membership, democratic discourse, citizenship, and the formation of public opinion and debate. You might consider a possible read.
When Abortion was a Crime 1867 - 1973
exerts of her book....
https://www.theatlantic.com/past/docs/issues/97may/abortex.htm