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.
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.