Most drivers focus on the fact that a green light gives them the right of way, regardless of what is around them. Green gives them the legal right to drive forward. However, it doesn’t guarantee that doing so will be safe.
Traffic engineers need to rig the signaling system to let people focus on the most basic condition of driving: For your sake and others, be safe. Increasingly, in Europe, they are addressing the problem in an unusual way: Fewer lights, stops, rules, and signals are better than more. Some cities are eliminating signs and signals at major intersections completely, based on the realization that individual, on-the-ground rationality works better than top-down rules.