> For example cars could go through intersections at full speed or close to it, timing it so they passed between each other. Cars could actually merge onto freeways and change lanes at full speed without some jerk trying to block them. You wouldn’t have slow drivers in the fast lane.
That kind of system precludes the presence of pedestrians and cyclists.
You'll still need crosswalks to allow pedestrians to cross the street. Beyond that, the mere possibility of a kid running into the street means that your theoretical maximum speed is basically the same as it is now, simply due to physics: even if cars can instantly detect a person trying to cross the road, you still need time to brake and come to a stop. That doesn't change whether it's a computer driving the car or a human. Speeding up autonomous traffic basically undermines the biggest advantage--360 degree awareness and faster-than-human reaction times--AVs should offer.
As for intersections where cars zip through the gaps between cars with minimal spacing, that's a pipe dream simply because you're cutting safety margins to nearly zero. Signals drop out and computer processes crash. Car sensors will pick up false positives.
Car brakes and tires wear down over time, which will cause the car's performance to deviate from what everyone's models will expect. Bald tires? Winter tires in summer? Summer tires in winter? Maybe your car tries to take into account tire wear, but what happens if they're out of balance or alignment and the tread wears unevenly? What about the autonomous SUV that's loaded nearly at its maximum load thanks to the home improvement supplies the person bought at Home Depot?
The sort of carefully choreographed ballet you're envisioning[0] falls apart in catastrophic fashion the moment a single car comes along that doesn't behave as expected. If one car slams on the brakes to avoid a kid, a ball bouncing into traffic, a barrel that fell over, or any of the million other examples of things that happen in a complex environment, you get a massive multi-car collision, and because we're now moving faster than would have been possible before, you're going to get casualties.
So you need to slow traffic flow and increase the distance between cars to create a larger safety margin. That cuts down on the expected advantages, and you wind up much closer to existing traffic flows than the imagined ballet. And even if we choose to ignore the possibility of failure, at the end of the day, roads are a finite surface. There's still a physical limit to the number that can physically fit on a given stretch of road. AVs could, theoretically, push that number higher by removing some of the factors that decrease capacity, but there's still a limit. They can't solve the problem of congestion.
There's also the human element. Even if you "know" the cars are communicating with one another and you'll safely shoot through the intersection, those pesky human brains--you know, the ones that evolved to notice predators on the edge of a person's field of vision before those predators managed to rush up and eat you---are going to positively lose their shit the second they see a car speeding towards them on what appears to be a collision course at 50 miles an hour. That kind of intersection is pretty much perfect for triggering those fight-or-flight stress responses, and they'll make the stress of even the worst of LA traffic look positively pleasant by comparison.
Can AVs do a lot to improve traffic? Sure, assuming they don't increase the number of vehicles on the road--which is unlikely, to say the least. Anyhow, even the less-capable levels of automation could decrease things like phantom traffic jams. But we'll never see the kind of traffic ballets you're talking about save, perhaps, things like highway on-ramps.
0. https://www.youtube.com/watch?v=fzkv5beS4uk