You won't see any improvements from AVs until human drivers are banned, after which the AVs can all drive at 100 mph and inches apart from each other. Traffic lights would also no longer be necessary.
Even if AI increases to great levels, inertia still would exist. A large truck cannot stop in inches when traveling at 100 mph.
The AVs could offer some advantages (ie cheap car sharing via resource pooling, reduced parking space requirements in urban centers) but safety or speed aren't part of the deal. AI isn't superhuman and AVs aren't able to brake the rules of physics.
All you need is an object of any kind, including a downed tree limb or falling rock, entering the stream of vehicles at an angle, to cause cataclysmic disaster in this scenario.
You forgot the most important factor: the exits. If the exits are congested because capacity is lower near the destination, there's nothing you can do in the road.
And most jams are caused exactly by this.
Hard to see how this could ever go wrong isn't it
And if we went fully AV, we could still do away with traffic lights for cars in cities, as long as pedestrians and cyclists have their own safe passages and/or AVs are smart enough to deal with them just crossing at will.
And no, electric engines won't solve this problem, at speeds above 30 mph the engine is no longer the major source of noise, it's the tires and the aerodynamic noise.
Except... it's likely that people won't own AVs of their own, so we'll be captive passengers inside a corporation's AV. That's a prime advertising opportunity. Why have an AV that gets people from A to B as quickly as possible when you can go at 55mph without needing to change the law and get double the time with the passenger?
How will pedestrians know when to cross the road? Will bicycles also become illegal?
Automatically re-routing traffic when the roads start being congested already works before that and it'll help a lot.