When I drive to work there is an empty transit lane for cars with 2+ people which seems to imply that most rush hour cars have just the driver in. If everyone is ubering in robot cars then they’ll probably share. It’s not that weird as people share public transport and choosing between $10 to get to work and $3 is a no brainer.
They might even Uber to the train station then Uber from the destination train station to work. Lots of ways of cutting traffic!
Values change. No one would take a taxi where the driver is just some unlicensed taxi driver. Back in the 90's that would be consider akin to hitchhiking in danger! Now we have Uber.
Also I drive because it's faster, and because once you go from A->B getting to B->C is probably easier. Not for privacy. Most people just need to get to work or school or their kids to school for the bulk of their car use. Kids to school might work by sharing with other parents you know.
Cars are different than a lot of goods though, because in and of themselves they are a wealth signal (at least in the US).
Most Americans don't really need an SUV or a pickup; a minivan or a sedan are more practical. Yet most Americans are buying them, because it makes them feel better about what they're driving and they want to show off. You may only take your car to the grocery store, but if you meet Becky from PTA in the parking lot and she has a really nice car that she owns, that's still a big deal.
Unless the ownership cost of a car were to spike significantly, this part of American culture seems hard to change, particularly when automakers spend lots of money making sure that Americans see premium gas-guzzlers as status symbols.
They might even Uber to the train station then Uber from the destination train station to work. Lots of ways of cutting traffic!