Honestly, driverless cars are going to reduce the total number of vehicles purchased because:
People will be able to subscribe to a car service. It will know your work schedule and have a car waiting to pick you up from home and job. If you want to go somewhere, you just let the app know when and a car will come. If you go to town to do some shopping, it will drop you off. You don't own the car. You don't pay maintenance. You have no car payment. You pay the monthly sub (and it can be different tiers, depending on how much travel time you need regularly.
Once most people start doing this, cities will only need enough cars to support the maximum transit demand at peak times. Some of the cheaper plans will offer rideshare, meaning the car will pick up multiple passengers that are going the same direction. The demand for owning a car will drop as it will be a bigger expense and feel cumbersome in time.
Parking lot space will be reclaimed and repurposed in cities (hopefully by making mini parks with trees and plants). Overall, cities will become healthier (since the vehicles will have cleaner emissions), with the air quality improving. Traffic accidents will be almost non-existent.
What you are describing here sounds a lot like transit, but instead of designing a city to work well with it or developing wise transit routes, we'll just let autonoumous cars fill the role and continue wasting resources with inefficient methods of traveling.
This will reduce the amount of cars parking, as well as the amount of traffic in general. It will remove noise and air pollution from cities without costing the city anything to build and maintain new infrastructure. While bicycles and clean mass transit is the ideal, most cities cannot afford expanding mass transit, and that still doesn't make a dent in the overall traffic and accidents. Also, mass transit has a limit to service area and stops. So mass transit can sometimes leave people needing to walk a considerable distance. If they went shopping at the grocery, they don't want to carry the bags to the nearest bus stop. They can have their automated taxi service do doorstep to doorstep travel. Mass transit is awesome and has a purpose and value alongside the auto travel subscription service. They can both exist and both provide value to the population.
A big part of the problem with cars is that their existing infrastructure is already very expensive to maintain and promotes other utilities such as electical lines and water lines to be longer and therefore more expensive as well. After initial investments most transit and active transportation ends up costing less to maintain per trip than car infrastructure. Currently much of car infrastructure is heavily subsidized.
I think there would also be issues with a significant portion of the population not wanting to adopt a subscription based service over private vehicle ownership.
Right now, there would be some resistance, but I think you underestimate just how much people are to used to subscribing to services. This includes hardware and software. If I lived in the city, it would be a no brainer for me. No searching for places to park (and pay). No worrying if someone breaks in to my car or vandalizes it. No having to take it to the shop for tune-ups and inspections and all that for cheaper than what it was costing me to own a car. If a car's purpose is getting me from A to B, it is still the most direct option in most cities. Take Asheville for example (I live here and know the area). There's a bus system. The trolley is for tourists. But that bus system will not be efficient for the individual both in time and energy, if that individual lives half a mile or more from a bus stop. The city cannot afford to add more and more bus stops to ensure everyone's home is near one. The roads are already in place, and would have to be maintained for the buses (and other services that use the road such as emergency, police, fire, mail, etc) no matter whether or no subscription car services exist. With cities that are VERY huge, mass transit already forces people to have to abide by a bus schedule as well as a work schedule. People want freedom of movement.
I'm very pro mass-transit. But it cannot be held up as the singular fast transportation solution for a society. The subscription service is not meant to replace mass-transit. It is meant to reduce noise, emissions and traffic at the benefit of more affordable transportation for those who cannot always use mass transit. For example, I might have a subscription that gives me a certain number of miles per month. Now normally, I take the mass transit to work, day in and day out, but maybe on the weekends I like to have a night on the town with my friends. The car comes and gets me, drops me off at the club right where my friends are. We drink, we have fun, bouncing from club to club. End of the night, I push the "come get me" button on my app and the car will pick me up and take me to my house. I can use mass transit, but also have reason to want a quicker option than waiting on the bus schedule. Nobody obsesses over what someone is driving. We're all just ferried around by the service.
And we have seen how fast populations will adopt something if you hit the right buttons.
Vehicles purchased might go down but vehicle miles traveled will go way up. The cost of driving will go down so there will be more mile driven and then there will be all the added trips of empty vehicles.