You don't actually need robotic cars for that though. Several cities already got car-sharing services, much like the bike scheme in New York (for you americans). Several of my friends already stopped using their car for that.
Car-sharing services are a thing, for sure, but they are by no means a replacement for taxi services or cars for at least a significant remaining chunk of the population, since they are (at least every one I've experience has been, at least) still node-based. And it's generally not cheap, either. Sure, they are convenient, and probably do enough for a limited portion of the population to drop the car, but for others they can't really replace what google is offering here.
Example: I, and almost everyone I know, at some point wants to visit their family. I, like almost everyone I know (in the US) have family that do not live a convenient place, and instead live in a place that will never be a feasible alternative for public transport. They are maybe half an hour drive away from the most optimistic presumptions of a public transport "hub". With the current car share program, even if there is a hub, I end up paying for a car for the entire time - upwards of six hours, sometimes multiple days - and this is
after paying for public transport to get me to that hub.
In the case of automated cars, I'd only be paying for the vehicle for a third that time worst case, and far less in the best case, and the time savings would also be significant. And I wouldn't have to drive, meaning I'd actually end up paying less in time costs for the trip than I would owning a car.
Finally, the car sharing services are only worth anything if you live near a node or have another way to get to a node - if I did, I could easily visit my relatives, but they would still need their own car to visit me (there's a reason many of them own a car just to drive it to the subway, and then take the subway around the city).
The benefit of the autotaxies is that every car is, in and of itself, a node. I guess it's mostly a matter of degree rather than kind (it sort of fills the same niche as the car share thing, it's just a lot more versatile and powerful), but for my relatives, a car sharing service will never be able to service them, but autotaxis could. Technically regular taxis can, but the cost would be astronomical, and it's cheaper for them just to own a car.