So if the cost of running your car is say $5000 a year and you can get an subscription robocar service for $100 a week then a large number of people will switch.
At the moment it's only cheaper to go car free if it's possible for you to walk/ride/catch public transport to work Mon-Fri and catch the occasional taxi when needed.
[1] http://exchange.aaa.com/wp-content/uploads/2015/04/Your-Driv...
There're already services that cater to those people. Full-service car leases, regular car sharing etc. People who want that already use them. But they don't seem to get that wide adoption. If shared autonomous cars would be adopted as widely, they wouldn't change traffic flow much.
It becomes even easier with a bigger pool.
Also, it breaks the driver/car connection since you are no longer a driver.
Finally, the real reason. Without a cab driver to pay and tip, cabs are actually cheaper than ownership. This is Uber's end game.
Car ownership requires at worst 1 car per person.
Carpooling requires a lot of planning and only works for with individuals with similar scheduled routes and requires the humans to include the time to drop off additional passengers or pass control of the vehicle to another for additional legs of the trip. Totally aside from the logistical nightmare it requires people to trust others with an asset worth thousands or 10s of thousands of dollars.
Imagine you pick 10 people. Getting them all to and from work shopping etc requires 10 cars at worst in the ownership strategy.
Imagine that carpooling might reduce it to 8 or 9. Its extremely likely that a route could be plotted for 3-5 cars to take all to their desired destinations both by moving back and forth for trips that don't coincide and by making slightly longer trips that move multiple parties.
Now imagine that you have the entire population and can match all the rides that coincide and include an entire range of vehicles including buses to get everyone from A to B maybe you can reduce this to 1-2 per commuter.
A fleet of taxis or cars from similar services could do the same. I don't see how the self-driving aspect changes the situation, other than possibly reducing cost by eliminating the driver.
Self driving cars by displacing the driver may eventually be cheap and flexible enough to compete with ownership.
I would think that applied to any shared cars, including taxis and ride-hailing services. Why would the self-driving feature reduce parking demand beyond that?