I agree with your scepticism about solving the commute traffic with a self-driving silver bullet. The research for traffic flow [1] says that, with human driven cars, a slice of a 4m wide lane will pass about 1000 people/hr in cars, about 7000 people on foot or bicycle, and about 10,000 people by bus.

That means that to get competitive flow with buses, self-driving cars need to deliver a tenfold improvement in flow. Since in traffic cars are quite tightly packed already, you probably can't get much from putting them closer together, so even if self-driving magic gives you two doublings of flow on its own you still need to more than double the speed limit to compete. I can imagine this working only on roads dedicated to self-driving vehicles, with no pedestrian crossings, so now self-driving cars benefits only materialise if they eat up a chunk of the public space.

You might get a bit of improvement from vehicle sharing as well, but it seems like a really complicated way to attack a problem that already has an OK low-tech answer, at least in high density areas.

Where I live the census says that about half the commute journeys in the area are less than a few miles, for which cars of any sort seem ridiculous to me, for the able bodied. For those who aren't able bodied or have a long journey all the able bodied car users on short trips are using up a scarce resource that they need!

Throw in the health benefits of active transport, and the health cost of particulate emissions (still a problem with electric cars, since a decent chunk comes off tyres and brakes) and it looks like a wash to me. Then again I am one of those awful bike people, so maybe I miss the point.

[1] Litman 2017, Brun & Vuchic 1995 etc.