The people who are driving, or at least a significant portion of them, pick driving over public transport because of perceived privacy and control.
I don't think uptake of shared mobility is going to be so popular where that becomes the norm.
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.
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.