In the long (very long) run it could solve this problem too - if all cars were fully automated and very safe, they could travel much faster even inside cities, thus augmenting the bandwidth of roads.
I'd argue that they can't go too much faster in cities. For starters, people live in cities and tend to walk or bike places. On a city street with no people walking around, sure, cars could go faster and be safe.
But in a city with people, cars will need to go slower and stop for people (or some combination). Even with instantaneous reaction, a car can only stop so fast.
