What would probably happen is that the price of a car would go up, which means more people will share a car (this would be feaseable with autonomous cars because you can still leave pretty much whenever you need to, and go pretty much where you need to, because you only need to coordinate with any other group of people who happen to need to leave at that time, rather than select the people you want to share a car with and then coordinate when you need to leave).

There is also the alternative that people will move further away from their work, because they can use the commute time -- essentially then, they would leave their homes at the same time, start working and then leave their offices so that they are home again at the same time, which means (assuming everybody lives at different distances from their workplace) that you automatically get a stackering effect.

Autonomous electric fleets can bring cars in before the predictable peak hours occur, reducing congestion. Autonomous fleets are also not vehicle size limited. You can bring in autonomous buses that go point to point (mostly) because there is high enough demand to fill such specific routes. Autonmous fleets are also not wandering streets looking for parking, which is a major part of congestion.

Autonomous fleets can also be parked in towers, because a robot car doesn't care if it takes 10 minutes to get out of a tower, as long as the throughput is high enough.

Eventually you will need heavy rail to increase throughput for dense enough places, but that's still a separate problem today.