Car usage is obviously directly tied to road usage. High road usage leads to congestion. In a sense, you want there to be a limit of the number of cars on the road: Just under what would start causing significant slowdown.
The fixed costs of owning a car are expensive, but typical city/suburban usage ignoring work commute easily makes the costs worth it. The time expense of using public transit or the dollar expense of relying on lyft/uber are simply too high.
Self driving cars have some advantages:
They reduce the cost of sporadic non-peak usage. For some this will make the work commute on public transit a dollars+time net savings. This pressure will be especially high on 2+ car households, where the economics of a second car will be abysmal.
Self driving cars can act as a much more efficient feeder to public transit. At any given time, especially during peak usage, there are a bunch of people going from approximately where you are to approximately where you're going.
We aren't taking advantage of this today because of two problems: Coordination is hard and requires a critical mass. Any time stopped just kills average speed, greatly increasing time to get to a destination (this is why busses are soooo sloooow.)
Self driving cars can take people from their houses in suburban neighborhoods to coordination locations. Hop in a small bus/shuttle with a few others. Wait no more than a minute or two as cars arrive. Then the shuttle takes everyone to their destination (if it's a high density city where the destination is within a block), or the reverse of a feeder, where single person taxis are already there waiting to take you, with a pause as long as it takes to get out of a vehicle, walk a few feed, and get in another.