I hate for a long answer, but if you want the answer to your question, here it is...
There is a general shortage of OBs in the country and an acute shortage in rural areas. There are so many reasons not to be an OB, that the only reason to be one is a passion for the specialty.
Enough of a passion to accept being sued regularly, to work horrific hours, and depending where you live earn less than other physicians with the same amount of training.
You simply have to love the specialty or it will suck the life out of you. We tried and had some success mitigating this problem in the groups I ran. But I had the advantage of being located in a suburban/ urban market with our OB practices (I have had PCP practices where they were the only health care in their county).
We organized our Ob/Gyn into a minimum size of 5 to 8 physicians plus midwives. This insured the physicians, that they would be off three week-ends a month and four out of five weekday evenings. However, to make this work operationally, you need to deliver between 100 and 150 babies a month.
With fertility rates just under 2 per woman, you need around 18,000 women between the ages of 18-40 in the area to support the practice if you are 100% of the market. If you are say 25% of the market, you need over 70,000 women between the ages of 18-40 to have a "women's health" model that works for patients and physicians (especially female physicians, who place a higher premium on spending time with their families than the average male Ob/Gyn... that is the truth, not misogyny).
So, you can see one problem right off, most rural areas are do not have enough women of the right age to support a large enough OB practice that can offer physicians a chance at a reasonable quality of life.
But it gets worse. You earn a lot less working as a rural OB/GYN then you do in a suburban area.
Rural areas are dominated by Medicare and Medicaid (38-43%) patients with fewer "private health insurance" patients. For OBs that is particularly tough, since "Medicare" patients are mostly seniors and thus not having babies, which means to high a percentage of your practice is GYN and most of your OB practice is Medicaid. Medicaid reimbursent stinks using Georgia as example Medicaid pays about 25% of what private insurance pays for the same procedure.
We had relatively low malpractice claims, but even then 50% of the money we got per delivery went to cover malpractice. The rest went 60% for office overhead and 40% for physician compensation. We made zero profit towards corporate overhead, which is why we eventually exited OB/GYN as a service. Huge malpractice risk with zero profit makes for a poor business model.
In many cases, I have come across rural Ob/Gyn groups won't accept Medicaid patients since after malpractice and office overhead, they are literally paying for the privilege to deliver a baby and like our company taking huge malpractice risk since Medicaid babies come with far higher complication rates.
Lousy quality of life (unless you are a workaholic) and low compensation versus what you could earn in a suburb with low Medicaid populations explains why rural areas have a problem attracting OBs...
Half (49%) of the counties in America in 2012 according to MedicineNet had no Ob/Gyn. None of these shortages were attributable to the recent Supreme Court ruling.
Georgia being slightly more rural than most states has 51.6% of their counties without a resident OB/GYN using your numbers from Stacy Abrams. A 2018 Georgia study put the number at 76 counties, or just below the nation's average. So, Georgia does not seem to be unusual or an outlier.
https://thegeorgiasun.com/2019/12/02/rural-health-care-crisis-nine-georgia-counties-have-no-doctors/#:~:text=Nine%20of%20the%20state%E2%80%99s%20159%20counties%20have%20no,no%20ob%2Fgyn%2C%20and%2060%20were%20without%20a%20pediatrician.
Now regarding why there is a lack of facility access, the answer is largely malpractice related. In the past, we had a saying that rural hospitals were emergency rooms with maternity wards attached to them, that did a little same day surgery on the side.
A bit of an exagerration, but not much. But the soaring cost of malpractice and the lower fertility rates of women has resulted in more and more rural hospitals closing down their maternity wards. Forget abortions, many are trying to avoid doing deliveries except in the case of "emergencies" and then they transport the mother and child if there is even a slight medical issue to higher level hospital.
To replace this lost business, these rural hospitals are adding outpatient procedures and treatments including diabetes management clinics, chemo units, etc. Basically, services that don't require beds. Even my local hospital in a town of 60,000 people closed almost 10 years ago. So again, abortion has nothing to do with why rural medicine is in the state it is.
Some major hospitals are acquiring rural hospitals as part of an integrated care model. In those models, the rural hospitals functions largely as "loss leaders" but provide the referrals for highly profitable "heart and orthopedic" patients.
Again generally speaking maternity care is not something most hospitals want but rather offer it as a service to their communities.
The problem of "rural medicine" is a challenging one. Abortion services does not really factor into the equation.
One reason why there are almost no abortion services in rural communities even in those states with very relaxed abortion laws is that to make an abortion facility financially viable the "catchment area" is even larger than what is needed to make an OB/GYN practice viable. That means finding a facility doing elective abortions is getting rarer.
In some respects the changing laws may help keep abortions centers viable by driving more cross state volume into their centers. The state that closed the most abortion centers (13) in recent years is California with the some of the most relaxed abortion laws. At the end of the day, abortion clinics are highly profitable businesses, if you get enough volume and you can "sell" the dead babies... again the brutal truth.
I hope that answers your questions.