Why do you think people using a driverless car service would care less about having to share their ride? In theory if people would just carpool much more right now, the number of cars on the road would go down a lot, and they could divide the costs. But somehow they don't.
I don't see why people who don't consider carpooling right now would order a driverless car that needs to pick up some other people before going where they want. So how would driverless cars reduce the number of cars on the road? Or to state it differently: why do we need driverless cars to get the average occupancy of cars on the road above 1?
We (as a society) are fully capable of building single-person cars. It's just the economics of car ownership incentivize having four to five seats and a lot of trunk space just in case you need it, even if you aren't using them 99% of the time.
That's likely to change if the cars are being run by a driverless car service. They'll already have the numbers to know how many single-person cars to maintain in the fleets as compared to five seaters. Fuel / electricity will be cheaper for smaller vehicles. If traffic does notably increase, tolls and congestion taxes will come more into play and be lower for smaller cars. Single person cars could split lanes (like motorcycles).
At that point, the economic incentives change, and we could see different outcomes.
Convenince has historically proven the industrial era and beyond killer app. Availability is part of the issue - it would increase car utilization but probably not people in a car at once. They would care less about "my car isn't available because it is out working" if they could get a replacement. They also don't need to give their time driving passengers.
Self driving also could allow better "microroutes" which don't take you out of the way like public transit. It wouldn't address the stranger adversion however.
Ironically in the worst case it may technically reduce the average occupancy even if the total utilization rises and thus number of cars on the road drops for the same demand.
Convenience. Habit. Cultural pressure. Regulatory changes. Etc.
It isn't as simple as "People don't do it now, why would they do it in the future?" There are many ways to make automated car sharing far more attractive to people than car pooling ever could.
This isn't a technology problem, it is a geometry problem. Car pooling/sharing cannot work very well because eventually the car needs to go down some "dead end" that you didn't want to go down to pick up/drop off somebody, and that time is wasted. If you are the last one on and first one off it is great, for everybody else it is wasted time where they are not making any progress getting to their destination. Everybody would be better off (less congestion - less expensive roads need to be built) if everybody carpools, but you are always personally better off to be the one person who doesn't.
It may seem like you can solve this by just picking up in the neighborhood. However there are not enough people in any given neighborhood to make that work. This morning exactly one person (car) passed me on my way to the bus stop - I don't know if this person would go the same direction as me or not: there isn't much opportunity for ride sharing within one neighborhood.
Transit has the same problems. It solves them by forcing people to walk to the stop/station. At least everybody feels like they are making progress. They also come on a schedule which means you can't leave when you want to.
I don't see why people who don't consider carpooling right now would order a driverless car that needs to pick up some other people before going where they want. So how would driverless cars reduce the number of cars on the road? Or to state it differently: why do we need driverless cars to get the average occupancy of cars on the road above 1?