Isn't "sharing a vehicle with a stranger" like, the #1 reason why most people who could use transit for a given trip choose not to? Why, when it's a way less efficient—and probably way more expensive per-rider-mile to the govt paying for it—autonomous car going to change that?
The issue with cars, self driving or not, is that they fundamentally use up too much space in urban areas, and cannot efficiently navigate crossings. The problem with traffic isn't (only) that cars are not full, but that in dense, high demand areas where paths/modes cross (i.e. intersections), cars make it extremely difficult to efficiently navigate that shared space. People and bikes can navigate without stopping, bus and trams move such high volumes of people that it significantly reduces the number of vehicles on the road (factor of 20x-40x). Heavy rail (and some light rail) is usually grade separated, and thus doesn't need to worry about intersections at all.
Self driving cars solve almost none of these problems. Unless you're imagining a future where existing outside of a car is illegal (and driving a car manually is illegal) and cars just autonomously speeding through intersections by choreographing perfectly in sync without crashing, AVs will still have to negotiate with everyone else, and thus they still have to navigate the intersection in much the same way they do now. Increasing the diameter of the pipe means nothing if the spout (the intersection) is the same.
So basically, increasing road capacity doesn't matter that much. If you still have a massive amount of individual vehicles trying to navigate the slow capillary network in an urban core at the end of the pipe, you're still going to have traffic on the highway into the city.