Most drunk driving accidents/deaths happen in rural areas because there is really no other alternative for transportation. Because of low population density and long distances taxis are basically impossible to find. Self driving cars could definitely fill a niche there should they ever become cost effective.
If the price is right, maybe. I live in a semi-rural area (about a house per acre, but unevenly distributed) and we have one Uber driver and a handful of taxi companies. Competition is tough though, my PHEV costs very little to operate and there's always parking and the bus system does on demand rides for $2 during weekdays between the morning and evening peaks.
I can't speak for the US, but in Europe (experiences from Sweden, Norway, Russia) rural areas usually have a handful of taxi drivers and you "use their services" by calling their numbers which you can get from locals.
In Finland we had a law that required the taxi monopoly to provide services even in rural areas, so disabled and elderly people could get transportation to services they need. Worked well in my town of 7 000 people except sometimes on weeknights the only driver could be in the next city 50km away.
(Had, as in they changed the law few years back. Not sure how it's now)
Robotaxi(s) could be quite good solution to the problem - the drivers were often pissed if you called them for a single ride when they were home or far away.
