In army you trust others to move with you.
In car, you know that others won't move anyway so you wait and react to their behaviour.
Army also moves in cohesive manner - unit is going towards known place.
Car drivers do not know where others want to drive.
Even the purpose of turn signals evade most drivers - they exist so you can signal your intention BEFORE manoeuvrer - most drivers turn them just before they need to, or even during the manoeuvrer.
In the army some chief gives the instructions. Everyone obeys the instructions (regardless of whether you trust or don't trust your adjacent soldiers to move as well).
Seems the problem really is just the lack of co-operation and individualism that produces a negative externality for the society as a whole.
Of course, in a fully autonomous road network this is both possible, and mostly unnecessary, as nobody has to stop at traffic lights any more. Apart from pedestrian crossings of course.