I think the societies that are culturally willing to embrace self-driving cars are the ones that already have better solutions. I'm talking about the downtowns of major cities, Silicon Valley, university districts, etc. In most cases bicycles, light rail, or buses are already being used and are more efficient than a million people riding alone in self-driving cars. If anything, these are the places that might ban private car ownership as population density increases.
On the other hand, no self-respecting country boy is going to want to give up the freedom and independence that he gets from driving his own vehicle. Separating yourself from the herd is a value proposition, and self-driving cars can't compete with it.
What's left?
1. In some cases suburbanites might use self-driving cars to get from the suburbs to the edge of the car-free downtown zone. It's possible the technology would work for them, but, do any of them perceive an unmet need? Is there anybody out there really frustrated by having to look at the road during their commute? I would think there's a lot more incentive to find ways to shorten the commute, than to simply make it hands free.
2. Interstate trucking is a possible use case, if people would tolerate it. You'd need a plurality of states to get on board with the idea of a very potentially deadly machine going on autopilot, and you'd need to sort out who's liable when people are killed by it. And you need to figure out the "last mile" -- who drives the truck after it takes the exit off the highway. There's a real shortage of truck drivers in the world, so this is probably the one market where there's a commercial incentive to develop the tech, though.