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Is this the root pathology behind traffic? Like, I never understood traffic, is there someone at the front refusing to go fast enough or is it the result of some distributed error like this that everyone mis-optimizes for that in aggregate results in traffic?
Based on a game* I think that the root issue is that there are multiple bottlenecks, unavoidable for the drivers, like turning or entering/leaving lanes, forcing them to slow down to avoid crashing. Not a biggie if there are only a few cars, as they'll be distant enough from each other to allow one to slow down a bit without the following needing to do the same; but once the road is close to the carrying capacity, that has a chain effect:
There are solutions for that, such as building some structure to handle those bottlenecks, but they're often spacious and space is precious in a city. Or alternatively you reduce the amount of cars by discouraging people from using them willy-nilly, with a good mass transport system and making cities not so shitty for pedestrians.
*The game in question is OpenTTD. This is easy to test with trains: create some big transport route with multiple trains per rail, then keep adding trains to that route, while watching the time that they take to go from the start to the end. The time will stay roughly constant up to a certain point (the carrying capacity), then each train makes all the others move slower.
You forgot one solution.
Teaching people how to drive safe and smart. Way too many people focus on the car in front of them instead of the traffic ahead. If you watch for brake lights as far up as you can see and let off the gas when appropriate, not only will you be less likely to be in or cause a wreck, you will also save wear and tear on your brakes and use less gas (even more pronounced with regenerative braking).
In addition to the above. When you are driving a route you know well, get the fuck over from which ever side is more likely to be used to turn off. For most highways this means moving left before you near an onramp. Plan ahead and get over before you need to do so you don't have to speed up or slow down to let people in.
Driving safely and smart is essential for other reasons, it does prevent additional bottlenecks (you mentioned one, wreckages), and it reduces the impact of the unavoidable bottlenecks (because the cars won't waste so much time re-accelerating after them). But if my reasoning is correct, most of the time there isn't much that drivers can do against traffic besides "don't use the car".