You are grossly overestimating the capabilities of single-system control. You've just described a far more complex version of the global flight management system. There are about 100,000 flights per day across the entire world. Los Angeles alone,
it seems, has four times that many cars per day in a single one of its roads. The global flight system is run by some of the best, most reliable computer systems we've ever built, and is still heavily dependent on human beings doing the heavy lifting. And unlike cars, it can avoid vehicle intersection in three dimensions, with far greater margins of error you find in any road.
The idea you could control all cars in a city with a single computer, with little enough delay in communication to make safe decisions (where decisions need to be made and applied in fractions of a second) is at this point sci-fi.
ETA: To illustrate the issue, what exactly do you think this computer would do if a child in a bike swerved into traffic? How would the computer 1) identify the problem, 2) calculate the rerouting for every car in the vicinity, avoiding them crashing into other already-calculated paths and 3) transmit the corrections to all vehicles that might be involved in the approximately second and a half it takes for that kid to be run over?
AI cars deal with this by each carrying a computer of their own, processing it's own visual data in real time, and driving defensively when it is called for it, and aggressively when it must. Centralizing the problem would require a computer that would dwarf google's entire operation, and it'd still be incapable of dealing with the sheer raw data from billions of vehicles all needing second-to-second decisions.