A challenge with “synchronizing” is that in general you can’t do it, even given infinite desire & resources.
If we assume a rough grid of streets with heavy traffic moving in all 4 directions, it’s simply mathematically impossible to time the lights so everybody moving in all 4 directions can maintain a steady speed and get in sync with a wave of lights turning green for their pulse of cars. For some combinations of speeds and distances between blocks it’ll happen to work for a few blocks; for most not. And the less grid-like the street pattern, the more likely you’ll hit problems.
To be sure, if your local traffic pattern is 90%, say, westbound in the morning & eastbound in the evening with much lighter N/S traffic at all times, then you absolutely can prioritize and synchronize the flows in the one major direction. But there are costs …
At some intersections there are lots of left turners. At those intersections that represents a restriction on the flow in the opposite direction, since they have to be stopped to permit the left turners across in front of them. At other intersections along the same route there are few left turners. For smooth flow of traffic in the predominant direction the duration of the green cycle at each light must be the same. So the need for differing length left turns drives a very big delta in the length of the opposite direction green. But you can only make the opposite direction green so short before it gets to be too short to be useful. IOW, you will eventually end up not providing enough green to support your total left turn demand at the worst case light. Which unserviced traffic then backs up into the through lanes of your predominant traffic flow.
Other issue: To make it easy for the predominant direction to flow, you want a long green light. And the longer it is, the easier it is for a car that’s marginally too early or late to adjust speed to get within the lump of cars traveling in sync with the greens. Essentially the traveling time-slot of green lights is bigger, with more happy middle and less problematic edges.
But the longer that green phase gets, the longer the red phase for cross traffic gets. And there’s always some cross traffic at busy times. So what happens if we make their red light longer than most folks have patience for? They start doing unsocial things like pressing late on their yellow and well into the red. Or turning right then left into side streets or businesses to effect a 2- or 3-step crossing of the main street. And usually doing these moves hurriedly & hence with poor safety. And even if they don’t cause a few accidents, they do inject turbulence into the predominant flow which all this green synchronization is trying to comb into fast smooth non-turbulent flow.
And what happens when the cross traffic green gets so short it doesn’t flow all the traffic on it’s road? It starts to back up, perhaps to the next block where it interferes with the predominant through flow in the primary direction on the next street over.
There are lots of other similar examples of theoretical & practical obstacles.
Bottom line: There are real physics & math obstacles to good sync. There are real behavioral obstacles to good sync. Managers nothing to make smarter light timing is an abdication of responsibility; but drivers expecting huge gains from smarter light timing is unrealistic. A few percent improvement is plausible, but that only offset a few years traffic growth & you’re back in the same situation.