Self driving cars don't solve high traffic volumes. Cars just can't move enough people per hour, I think the average lane can move about 1800 cars per hour and most people don't share rides unless forced to. So that means about 1800-2500 people per hour per lane. A decent subway moves about 20 000 people per hour per line, I think.
Cars are low to medium density transport, at best.
That wasn't true in the past. My father used to carpool with other teachers for 20+ years. I remember a lot of carpooling through the 1980s and into the mid 1990s where it fizzled out.
I would suggest, however, that self-driving cars would be fine for carpooling. Most people would have no problem carpooling with a self-driving car if it always picked up the same bunch of people every day. If I can commute in 35 minutes or take a self-driving carpool for 45 because it stopped to pick up 3 other people from my department along the way, that would be fine.
People got into carpooling because of the oil crises. Then the oil glut happened, things got cheap again, those carpool groups broke up, and it became uncommon again.
Cars are low to medium density transport, at best.