Cronk, you make it sound like some socialist utopian dream. Our car improves our lives, giving us a freedom that is otherwise impossible.
A trip to town will take me 20 mins, on public transport it is 1½ hours. Car systems will be as long, or longer because of the wait and availability.
Your system by definition will require the involvement of many people and organisations. Everyone involved will require paying, increasing your costs year on year. Just as the tax and power costs of electric cars can only go higher to cover increased government involvement.
This system is put about a bit like the total fallacy of interest free borrowing. The claim that you can buy something over several years without any interest charges is simply a nonsense. The fact is that the interest has been added on at the start, before the product goes on sale. When you buy it the total debt is passed to a finance company who refund the seller the total, less their agreed interest and management charges. If I buy anything I'll just want to pay for it and that's the end of it. If the deal is interest free, then they want to charge me interest even though I'm paying in full at the point of sale. So if it is an interest free deal, then I'll want at least a 20% discount, or I'll walk and they lose a sale. Like I say, if someone else is involved, they'll want paying.
The the initial car cost plus ongoing software, management fees and maintenance, plus callout are all to be added. You are basically hiring a car. The costs of which will be higher than a taxi. So in your new socialist world how much for a day out? Say 50 miles away out in the sticks, miles from anywhere? And how good will it be if you finish your day out and a car isn't available for another two hours or more? Or possibly not even until tomorrow....and it is raining, super! Rest assured if your car doesn't appear you will not be able to speak to anyone about it, a robot will not provide as solution.
Just going to the supermarket will require you to book and wait to be taken. Then when you have your groceries, repeat. So the trip to the supermarket will become three hours or more instead of an hour to go and get back. Plus the car park will have to be totally redesigned to allow the necessary queueing system to work at busy times. But every minute of that trip you will have to pay for. Plus a car for one person will be a fraction of the price than for one for the whole family. What do you do if you want to drive around in a Merc or BMW and they send you a tiny Peugeot?
There are 36 million cars on the roads in England. Some in remote hamlets and some in cities. What series of conglomerates responsible for the socialist car will be able to manage that. Plus, government will be heavily involved and we all know that everything governments' are involved in are a dog's breakfast. This is then all in the tight grip of the FANGS, who are in the main, often socialist dictatorships. It couldn't be worse.
In the real world it is simply not practical and is a total nonsense to imagine that it is. It really hasn't been thought through, or it's a huge con. Which I think it is.