>Reducing the (perceived) need to buy a car, e.g. by making it easy, cheap and reliable to get from A to B using a self driving car service

But this assumes the need for a car, but cars are one form of transport. A more wholistic look at transportation with be “Reducing the (perceived) need to buy a car, e.g. by making it easy, cheap and reliable to get from A to B.” If you have more services within walking distance, it reduces your need for a car. If there is lots of bike infrastructure, it reduces your need for a car. If there are reliable frequent trains, it reduces your need for a car. If there are reliable frequent bus services and bus lanes to get around traffic, it reduces your need for a car.

On the other hand, if there are more cars then you need, at minimum if we imagine self-driving cars, more road capacity. But realistically more roads and more parking. More space for roads is less space for the actual places people want to go, pushing those things farther apart. Being farther apart reduces the number of places you can get to by walking or biking, which means you are more likely to need a car, which means more cars, which means more roads, which means less space for the actual places people want to go, repeat. Cars are basically the worst option in terms of infrastructure cost, land usage per person, personal cost to use/operate, deaths and injuries, etc.

This assumes the occasional need for a car, because even with the best public transit etc. in the world, there will be cases where not using a car is impractical.

If you need a car on at least a weekly basis, you're probably going to have your own car either way (unless the self driving car services are really good and cheap).

But even if all everyday trips don't require a car, it's very likely there will be some exceptions. And those can make or break this. If getting a car for that occasion requires hours of overhead (e.g. getting to a pick up/drop off point), is sufficiently inflexible (cars not reliably available on short notice), or prohibitively expensive (e.g. per-km charges on car sharing cars that make a couple longer day trips per year more expensive than just getting a cheap car), people who otherwise could do without a car will consider getting one.

OTOH, if the alternative is really good, people who occasionally need a car might use a service rather than owning a car, which means usage-based cost i.e. a much bigger incentive to pick alternatives. If they have been pushed to own a car, the fixed costs are a sunk cost and the marginal cost of taking car can easily be cheaper than public transit.