Why would it be so hard to drop the car seat requirement? Taxis are exempt from them, the security benefits are questionable already (more so once you factor that an autonomous car would probably have a different cabin and safety features), buses and trains don't need them...
Not to mention that a society that gets away from being car centric would also grant more independency to children from their parents. In Japan, kids are used to go to school by themselves at age 5. In Berlin I see kids seemlingly from elementary school going around alone in the U-Bahn. Looks like parents not having to be kids' chauffeurs would be a net gain.
You'd have your own private autonomous car. You could keep the car seats, clutter, etc in it.
It would drive you to work, then it would drive itself home and park there (or at an out-of-town free space) instead of parking in the city.
Later, it drives itself back to your office to pick you up.
No shared car required, no parking space either.
Or do you expect parents to attach car seats each time they call one up? And where do you put the car seats the rest of the time? Cary them along with you?
It would be nice if the cars came with them built in, but I don't think it's possible to make a seat that can accommodate every size child.