Let's say each ride cost $10... that is $20 to $40 per day just for the kids on most weekdays. Add in birthday parties, saturday games, doctor/dentist, trip to grandma/grandpa that live 7 miles away... and we are talking $1000 per month in "ride-sharing costs" for my children alone. We could add in my wife and I's costs, but it would be silly.
Maybe this service is less than $10 per ride, even at $5 per ride it is wayyyyyy more expensive than I currently spend on a 4 year old Toyota Highlander with low miles with insurance and fuel.
a.) Snacks and supplies in trunk - lockable containers inside. All could be accessible via app/key fob only.
b.) Who says the suburbanite your renting to won't want to use a car seat?
c.) Camera, ID, cleaning deposits, car self-drives to detailer on your lunch break.
$1,000 a month is a heck of a carrot to keep a car clean - even if that's not for you is your worldview really so small that you cannot imagine it being for someone not all that dissimilar from you?
If the total cost of ownership is, say, $1000 per month, you might only pay $200, or about $2.20 per ride.
Because you don't need to own the car - you could feasibly rent one on demand (like a taxi), since you can now rent a car without the necessary wage overhead of the taxi driver, or the minimum costs of car-rental (i.e. car rental typically is per-day, for logistical reasons) or the logistical problems of car-rental (i.e. you need to drive to and from the car-rental place, to pick up and drop off the car - and by "drive" I mean "get a lift or use public transport").
Plus, the self-driving stuff shouldn't be particularly expensive, and will be counterbalanced by lower insurance premiums, and likely tax incentives once voters realise that they really do save lives.
"Why does everyone assume the cost will decrease with scale? How many people can afford a Tesla right now? Let alone a fully autonomous car?"
Because just about everything decreases with scale, and it's not inherently hard tech. Tesla's main problem is their lack of scale. As are autonomous cars.
"Why does everyone assume that most people want to share a vehicle?"
Money. It's not "want", it's "can tolerate so as to save money". Your car, when adding together all the costs (purchase, fuel, rego, maintenance, interest payments if you borrow instead of buying outright) is one of the biggest expenses that most people have. Sharing a car between several people should decrease the costs by an order of magnitude, which could be used to buy whatever people spend their money on these days, or saved.