There is no time at which all cars are in use. So there this isn't a problem that prevents that future vision from improving on the present.
My observation is in the place where I live that around first morning hour the people who drive are the people who would use the car whole day. So we can ignore them in the estimation.
Then comes the bulk of the people who use the car to just get to work. I would estimate that around 1/2 to 2/3 of the cars are in the move during one hour.
I would assume that sizeable proportion of the current public transport users would also consider to use cars when they are readily available.
So I would assume that the number of cars needed to provide reliable automated cars service instead of private cars would be close to the number of current cars.
If it's environmental, we can assume cars in the future will be all-electric, powered by nuclear or renewable energy sources.
If it's congestion, firstly we should see a dramatic reduction in the number of accidents. Automated vehicles will make far more efficient use of limited road capacity, and with no need for parked cars to litter urban streets, we will have greater capacity.
More importantly, we can just regulate against congestion. Cap the number of cars in an area at any one time, if you want, or implement dynamic pricing. That will go a long way to eliminating unnecessary journeys during peak times.
Price or rather TCO. That is, if the amount of cars needed is the same as today, then why should people prefer communal self driving cars instead of personal ones?
Of course same cars could be used during the day, the question is just how much it would bring the cost down.
That will go a long way to eliminating unnecessary journeys during peak times.
Or eliminate the idea of communal self driving cars. There are no unnecessary travel when you have to get to the point A on time.