Cars already do talk to various traffic lights via underground sensors and occasionally a camera. The investment required to have a fully networked traffic light system with a centralized controller would be immense, and would create an organization with a natural government given monopoly.
Your use of 'correctly' paints a world that seems ripe for more corruption and ultimately worse timings across the network. If you wrote 'better', then I wouldn't have commented. I think I'm nitpicking