Regular cars aren't scalable at all. AVs are not any different than regular cars. In fact AV will increase the amount of cars on the road as more people that can currently not drive, such as children and the elderly, are now more likely to use a relatively low occupancy AV. So we can expect transit to get worse as AVs become prevalent.
The only scenario where AV may scale better than cars is if we're talking about autonomous buses, and that will only perform better if they are given the other features of public transit, such as dedicated lanes, which require set routes, and we're pretty much just talking about public transit in general at this point.
This picture makes it clear, for the most part. Public transit is a pareto improvement on personal driving pods in terms of scalability. Especially for fixed commute routes.
