I don't know where you live, but where I live the highways have lots of stopping during busy times. And of course drivers always have to be aware of stopped cars as they do happen. I suspect highways are where the automated cars have the easiest time, and it is far more likely side roads and suburban areas that are more confusing. Abrupt stops are more likely there (eg kids/pets running across the road). In the US I do believe that running into the back of another car under almost all circumstances makes you at fault.

Where I live a panic stop in heavy traffic on anything called a "highway" could get you killed. I imagine a lot of the stops we see on the highway that do not result in accidents are made safer by the network effects of lots of cars doing the same thing over time and communicating visually. It's different in nature than somebody (or some machine) getting confused and stopping suddenly in the middle of the road.

Don't get me wrong: things aren't so grim for the "just stop" approach of dealing with a problem. There's no reason an automated vehicle won't be able to communicate with other cars, warn everyone of an emergency stop (at a minimum), even find the best path off the road, depending on how serious the problem is.

Not if all of the cars can do it just as easily.

I love the mental image of a whole highway full of cars slamming on their brakes to let a leaf blow by.

How would a full switch to automated cars work anyway? Would they require different roads?

If their functionality included stopping on a dime at a duck on the road, and human reaction speed isn't equivalent, it isn't safe to human drivers. But cost and manufacturing has to factor in before we can just replace every car on the road. People still drive 20 year old cars.

I expect it will be a mixture of carrot and stick like any good phased replacement. Dedicated lanes (since they can drive 2ft from the car in front) and higher speeds because they are able to cut the reaction time down so much lower.

Eventually making it mandatory for some classes of roads (motorways / highways).

At some point in the very distant future your classic car will only be good for showing off on track days or classic car meets.