If you have a city (or portion thereof) laid out on a grid, you can operate it entirely without traffic lights. The idea is, each city block is a rotary. The rotaries fit together just like a field of gears:

At each intersection, all traffic turns. This means you can't move between places by getting on the street you want and just following it. Instead, to travel paths parallel to the streets you need to weave:

Note that if you want to go diagonal to the streets, as blue does above, this is similar to now. Travel distance between any pair of points is H + V + |H - V|. That is, horizontal distance, plus vertical distance, plus the difference between the two. The extreme cases are the red and blue paths above. In the red case, V = 0, so travel distance is 2H. In the blue case, H = V, so |H - V| = 0 and travel distance is H + V

I don't know how well this would work in practice, but I think it would be pretty good. You substitute constant speed for stop and go, which should minimize both agravating waiting time and inneficient acceleration. You do have a lot of merging, as in the case where each street has two travel lanes you have people going different ways wanting to switch lanes:

Unlike other rotary systems, this does not fail when different directions have hugely different amounts of traffic. Travel consists of moving straight, turning with the road, and merging. In none of these does an unequal traffix flow mess up the system.

Another concern is that this would be tricky for bicycles or pedestrians. I think this works ok for bikes, in that they ought to be able to complete the merges safely, but this would need to be seen in practice. As for pedestrians, we could continue to use the current walk lights, though keeping lights just for that purpose seems silly. Maybe a pure crosswalk system would work? I should ask a traffic engineer.