This is my thought also but the question is how big is the ratio between total number of cars and the cars in use during very limited time frame (mornings, evenings).

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.