One answer is unshared cars, or shared only within a possibly extended family.
Not all Americans are atomized urbanites. Many are in families.
My MiL, wife, myself, and my two kids could easily share one self driving car although the number of miles traveled would likely be staggering.
If my kids destroy "dads car" they are in big trouble, and "dads car" has "car alexa" and she will yell at them for awhile if they misbehave and god help them if "car alexa" has to resort to facetime dad at work to mediate a child argument. "Wait until your father gets home" worked on gen-xers when they were kids, but now we have facetime and dozens of equivalent systems.
The mileage used and CO2 footprint will likely be much higher than individually owned cars because every trip everyone takes will be twice as long upfront, plus my kids will be car mobile which means much less sitting at home (Hey, you want your allowance, have the car drive you 10 miles to grandma's house and rake her leaves while mom and dad at work and behave yourself because Car Alexa has her eye on you and I will ask her). Also my senior citizen MiL would never road trip at her age and driving ability but a self driving car would result in a lot of visiting rural relatives and doing stuff in the hypercongested and terrifying to drive in downtown. Heck if I had the car at my beck and call why would I ever eat lunch at my desk when I could hang out at a nice park instead and never care about parking or driving. Hey why drive the whole family to the library when you can just send all four separately at their convenience, each of which takes twice as many miles because its pick up and drop off service unless no one else needs it, for 8 times the number of miles driven. I need a head of lettuce for dinner tomorrow, normally I'd get it on the way home from work for "free" ecologically speaking, but my son is just doing homework on his ipad so I'll send him out shopping on a special trip because he can do his math homework for 90% of the time while the car is driving him.
I would realistically estimate we're doing about 25000 miles per year across three cars and if we replaced it with one extended family self driver, I think it quite reasonable we'd knock out 60000 miles per year. Given that the self driver is likely to be staggeringly more expensive than any of our three cars, it probably cheaper and better for the environment to have separate cars, at least until self driving is so cheap its "free".