Drivers should be paying attention to their immediate surroundings while stopped. Especially because the signals may change, or they may need to move for emergencies services or to evade a careening car heading their way.
And also to not incite road rage from their fellow drivers because they are sitting stopped at a green light. You could also cause a fender bender because other drivers, who also may be distracted slightly, are expecting the cars to move and then are startled when they look away for a brief second because the car in front of them had to brake for the car stopped at a green light. Some states hand out tickets for being braked at a green light.