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.
> most people don't share rides unless forced to.
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.
But I do think you are on the right track. I think public transportation in the form of buses doesn't make a lot of sense. But if Musk had been able to deliver on his promise of self-driving cars, then a giant city operated (or at least funded) fleet of small autonomous vehicles offering door-to-door service and route flexibility could change everything.