One of the problems I see with your scenario is rush hour. A company needs enough cars to meet demand for rush hour and peak travel times. The rest of the time a sizable amount of the fleet would sit idle.
“A company needs enough cars to meet demand for rush hour and peak travel times. The rest of the time a sizable amount of the fleet would sit idle.”
All businesses experience this. But cars will be far less idle than they are now. In a cost-per-mile scenario, peak miles will probably cost more, which will serve to increase non-peak usage.
Uber functions 24/7 in big cities around the world. They also do delivery during non-peak hours. A service like theirs will not be able to meet everyone’s transportation needs with self-driving cars, but they will probably put a big dent in it. And car sales to consumers will probably decline until that is a very small percentage of cars on the road.