In Manhattan, only 23% of households own cars (https://www.nycedc.com/blog-entry/new-yorkers-and-cars).
In suburbs, it's 100%+.
Are Americans living in suburbs 5x more freedom loving than those living in Manhattan?
Of course not. In suburbs owning a car is a necessity (regardless of price). In Manhattan, you can live without a car and space is in such a premium that owning a car is an expensive hassle. You can see how massive effect of price and convenience can be.
Now imagine that long term per-mile cost of using a car from a fleet is lower than buying your own car? Most people will switch.
How is that possible? Cars are idle, on average, 96% of the time. If a fleet of cars can generate 50% utilization (12 hour out of 24 hour day), there's a lot of room to make a profit while charging lower per-mile price than owning a car.
When self-driving technology works, it'll be a matter of time for majority (easily 50%+) of people to switch to using a car from self-driving fleet vs. owning a car.