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.

There is typically an acute need and it is a market that is chronically underserved, but also typically unattractive from an operator’s standpoint

Absolutely! I live in outskirts and I would LOVE to be able to get a taxi to the pub and back! Unfortunately they don't service me here.