Looks like the maximum distance is about 50 miles. Pretty good coverage, IMO.
So, let's post a map that actually illustrates concisely where there are no driver's license services, instead of a misleading one that shows all services and makes it look like less of a problem. Disproportionately, it is the Black Belt counties that have had their license offices shut down. The official argument is that these areas are poorer and have less tax revenue. No sh**t. So let's require a government ID in order to vote and ensure the people who have the hardest time obtaining them have to go further than everybody else in order to get it, instead of chalking it up to the cost of doing business within the arcane parameters that they've established. It is strategic, and not seeing that is clearly indicative of hackery.
You say "you've lived in the South", but at the same time, seem to think that the overwhelming majority of predominately black, poorer and rural people can just hop into a vehicle and drive 50 miles like it's nothing. If I didn't know any better, I'd think you were approaching this from a completely different mindset! If they could, they'd likely already have a license. Not having a license is indicative of not having reliable transportation and/or the funds/documentation necessary to get one. I'm wondering if your previous argument holds up: would you drive someone 50 miles + gas for $10?
Let's just assume that have access to reliable transportation. Maybe they decide to drive illegally to the DMV, or maybe someone takes them. We'll say $5 - $10 for fuel, and a 4-year license is $36.50. We're getting awfully close to $50 already. Hopefully, you don't need a birth certificate, which is another $15 in Alabama. There's a less than insignificant segment of those without driver's licenses who are in the situation because they don't have birth certificates. In another 10 years or so, they won't be a problem for the most part, but they still are today.
10% of whites don't have a photo ID.
25% of blacks don't have a photo ID.
10% of whites are in poverty.
25% of blacks are in poverty.
Most people have a photo ID. The ones that do not have them, don't have them for very specific reasons and because of limitations that most people would consider mere inconveniences to be shrugged off. This isn't rocket science. Anecdotal experiences and bootstrap arguments don't solve the problem, as they hardly ever do: poverty is the determining factor.