So making cars public, letting people just summon one at will to bring them where they want to go, cars that rides in coordinated, self-scheduling fleets, cars that pick up other people going the same way etc. etc. will lead to MORE cars on the road ?

Nope, not buying it.

For a shared car that you can summon, any road-mile it spends between a drop-off and a pick-up is a new road-mile created by swapping 2 parked cars with 1 moving shared car. These have to exist by necessity as well since trip demands are very uneven.

I wouldn't bank on ride-sharing either. Only a fraction of ride-calls are shared, and ride-calls are of course on a fraction of road traffic compared to private vehicles. Ride-sharing is probably going to be less popular in autonomous cars since you don't have the driver to act as a buffer with whatever weird stranger you can end up with, and the financial pressure to share a car is lower when you have no driver to pay for.

I don't personally think the shared-fleet model is going to be the dominant one. I think private ownership will. Which means you still have to deal with parking and such. But it no longer has to be at your office. (Why private ownership? Because if you need something every day, and you can already afford a car, you're gonna want to still have your own personal one and never have to think about not being able to find a ride due to a demand spike, or rates going up, etc.)

Today if you drive you have to actively sit in traffic.

Replace that with a commute in an isolated near-soundproof private office with a comfy chair, fancy sound system.

You're gonna see people who can afford it choose to take the luxury ride over standing packed in a bus or train.

You're gonna see people who lived 25 minutes from their office because they didn't want to lose more than an hour total a day driving start be willing to put up with a longer commute to get more space for the same money, since the commute is now idle alone time, to work or relax as desired.

You take away the biggest negative about something that is seen as a luxury good compared to the alternatives in most of the US. You're gonna get more usage.

It will probably lead to more cars traveling at any time, but potentially far fewer cars parked.

However: turn most of the street parking into bus and/or bike lanes, the parking garages into apartments, seems like an absolute win. (Except for Chicago, which is presumably going to have more problems with its privatized street parking.)

Then you are blind. It has already happened.

Look at commute length. When families had a maximum of one car, you simply couldn't live very far from work. As soon as you got two cars per family, commute times and traffic exploded.

If you can simply sleep during the trip, how much further will people be willing to commute? I suspect quite a bit.