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.