It's going to shift a lot of capital that's currently tied up in owning and maintaining cars into other uses. Right now, most cars are only in use for about 5% of their lifetimes. When everybody owns their own private car, those cars spend a lot of time sitting parked. If those cars could drive around and be used by other people who need them on demand, you'd need a lot fewer cars, as well as a lot less parking.
There are so many things I can think of. The taxi/rental/on demand model is far more likely to happen because who needs to own a car 100% of the time. Ride sharing is also easier - I suspect many people would be happy going a few minutes out of their way for halving the cost of their journey. (Computer systems would automatically manage supply and matching demand, as well as pricing.)
Not only do you need less parking for fewer cars, but you could have less parking for the same number of cars. For example there is no need for stores to have huge car parks - customer and employee cars can go and wait somewhere else and only return to the front door just as you come out with your goods. This can lead to far denser human centric areas.
Some roads can actually be decommissioned. Vehicles can load balance across existing alternatives and respond far quicker to developing bottlenecks. Occupied vehicles can be given priority over shorter routes than non-occupied ones.
Deliveries can be done without drivers. For example the delivery vehicle can drive to your home, work or anywhere else and you enter a code to get your items vending machine style.
It will give people greater freedom. For example if your vision isn't acceptable, or you have physical issues then it won't matter. In general the maladies that come with age won't affect mobility anywhere near as much as they do today.
Drives can be over longer distances as there is no driver fatigue. Perhaps there could be sleeper cars for when you want to go somewhere overnight.
Heck they can even do things like deal with you in the vehicle while you are driving to an airport or a border. You could show your passport, answer questions, check luggage etc. And then go straight through the border or walk straight to your gate at airport, or even be driven to a closer access point to the gate.
And I suspect we never get flying cars out of this. When the two dimensional earth surface is used so much more efficiently, why expand into 3 dimensions? And since we can increase the speed the more vehicles are automated, what advantage does flight have?
Yes, it seems unlikely that the same car could be re-used for multiple trips. However, you could move the parking lots far away from the places people want to go because the car could drop you off at the door and then valet itself to a remote lot. That would at least free some of the very valuable space currently used by downtown parking lots.
Nobody is talking about replacing a car part of let's say 100 with a car park of 5. If we could just replace it with a car park of 50, which with current travel patterns is perfectly reasonable, that would be a tremendous gain.
The "lot less parking" will do wonders for urban landscapes. When I travel through cities (including my own) and land that could be used for parks or habitation swallowed up by parking space, it seems like an incredible waste.
Though this presents a problem in that we're burning through a car 20 time faster, (100% vs 5%). Most cars people own don't last 20 years, so they won't even last a year in the future? There better be some distributed economic system for providing those cars, because that's a large expense.
A car right now needs regular maintenance as it is every few months, even if it's just changing the oil. That will go from months to days if they're being used 24/7.
Actually a car that is driven frequently holds up better than a car that is only driven every now and then, and is left outside for the rest of the time. Cars in almost-constant use will also be taken care of better, and automatically; for example, they will be driven through a car wash automatically regularly, and the automatic oil monitoring system will replace said oil at a machine during 15 minutes somewhere at a point where the demand is lowest. Maybe we'd be burning the car 2 times faster, I don't know exact numbers - but it surely won't be 20 times, and for any multiplier lower than those 20, we come out ahead.