I think your scenario is wildly optimistic. There will be times when you want/need a car on short notice and there will be none available, that’s inevitable. Think rush hour, for one simple example.
There will be no way a company can have literally millions of cars sitting around to satisfy demand during rush hours and have a vehicle less than 5 minutes away from everyone, at all times, only to have those cars sit the other 20+ hours a day not utilized, as the average passenger car is used.
And where exactly do those millions of cars park, especially if they’re electric and need charging?
And anyone who’s ever regularly used taxis in the past know about other passengers and their filth. I used to be in taxis twice a day 5 days a week for years and it often sucked - previous occupants coffee spilled on the seats, garbage, the occasional whiff of vomit, boogers on the back of the passenger seat (I **** you not), not to mention those who hack and cough their germs everywhere ....and this is with a driver who should be a deterrent for this sort of stuff, as well as cleaning up occasionally. Can you imagine a situation where there’s nobody in the car to even care about all this before you and your family pile in?
It ain’t gonna happen for a very, very long time.