As for everything else, I totally get that not being able to keep stuff in your car is inconvenient. But there are billions of people out there who don't own cars who already deal with these issues every day, and they can be overcome. For instance, I live in NYC and I don't own a car. When I'm out of the apartment for longer periods of time I bring a backpack with me, packed with water, a Kindle (for amusing myself on subway rides), additional clothing suitable for the day's weather, an Anker battery pack to recharge my phone, and other stuff.
The big advantage is that you are no longer paying the substantial costs of car ownership, which should more than make up for the slight decrease in convenience. If it doesn't for you, you could always buy your own self-driving car.
Some people seem to be very hyped up by autonomous driving and think that most people would jump on that bandwagon. I'm giving perspective that a big chunk of population have reasons to buy their own cars. It'll definitely boil down to price of the service. Would I drop convenience of having my own car for 80% car budget saving? Yep. 10%? Meh.. 50%? Maybe.
The "substantial costs of car ownership" depend on car. If you want to have (almost) new car, then yes, that's expensive. But after the car is paid off (or you just buy used with cash), car ownership isn't that expensive. Car sharing seems cheap compared to new(ish) car only. It's worth to own new(ish) car if you drive a lot and/or car must be available immediately 24/7. But car sharing service won't cut it for you then. Or if car is more than a mean of transportation. Car sharing won't fit the bill either. Unless autonomous car sharing would be few times cheaper than current car sharing. Even including all the junk miles.
Same with commuting or going to mass events. I keep some drinking water (fuck stadium/concerts pricing) in my car. I keep some gloves in case weather is colder than expected and to make sure I didn't accidentally forget them at home. Ditto on umbrella. I always got some reusable shopping bags in my trunk. Fuck paying for shitty plastic bags at grocery shop.
My mom's trunk is literally full of random crap that she uses maybe twice a year. But she loves having it there.
Using random cars (wether self-driving or not, e.g. regular taxi) would have to be much better to payoff for loosing this advantage.