We see current cars marketed based on their safety features or crash test results - in this driverless future we'll have luxury brands touting that their remote drivers are based in the USA and can respond 5 times faster than more affordable brands with drivers on the other side of the world.
If you own the car, you'll be the one responding to it. But if self-driving cars work as well as they're hoped to, you won't own the car. Car ownership is absurdly expensive.
I mean, it's absurdly expensive except for all of the other types of car usage right? Companies have been pushing car subscriptions for years because they sound nice: "Don't worry about maintenance, just pick a new car every so often!". Except that it turns out to be even more expensive than just owning a car.
Leasing (unless you have some tax advantage) is typically more expensive than owning.
Ride hailing apps are great, but I don't know anyone who has run the numbers and decided it makes more sense for a daily commute than owning a car (maybe someone with no or extremely expensive parking options?).
I'm skeptical that using a self-driving car service from a profit-seeking company would end up being less expensive than owning your own self-driving car, but maybe we'll see.
Leasing and car rentals have the same problem, which is that you're a single driver hogging an expensive capital asset that you'll use maybe 5-10% of the time. This low capacity factor makes car ownership very expensive. The presumed advantage of self-driving cars is that self-driving vehicles can operate at a higher capacity, factor without incurring the extra costs of needing a human driver to operate them (like taxis) which will make them more useful.
NB: I did not used to think about this much until I recently went to price an extended warranty for my low-mileage car: all of the plans were denominated in years _or_ miles, which meant manufacturers price maintenance in terms of years owned, regardless of usage. The same is true with insurance, which is a huge cost for most drivers: some insurance plans offer a modest discount for extremely low mileage drivers, but to a first approximation the fixed costs of simply owning a parked car are huge. Basically the only saving for owning a parked car is fuel (which can often by offset by the cost of parking, whether that's born by the owner or subsidized by the city.)