I hate how much space in cities is devoted to cars, and I wish we had much better transit of all sorts.

But - I'm just not sure your analysis is right. Someone who drives a self-owned car will park it in a downtown area for hours. Someone who takes a taxi of any sort will use much, much less amortized parking spot space. New York is a pretty good example of this.

Good public transit beats the snot out of cars, but a dense taxi deployment seems to get more people moved per total car-dedicated-space than private car drivership does.

And if we can reduce the amount of space dedicated to parking, we can increase density, which reduces the need for driving.

So the problem will be if we have self-driving whatevers at the expense of public transit, but perhaps not if it's at the expense of private car drivership.