The law as written and the law in practice, are different matters.

NYC would not function with actual adherence to the law.

There is never a break in pedestrians long enough for a car to turn in a fully legal fashion at most intersections, which is why human drivers wait for the largest mass of the built-up crowd to go and then inch their way through the stream of those just arriving at the intersection (with pedestrians seeing what the car is going to do and then flowing around the car). Technically, the pedestrians have the full right of way.

On the pedestrian side, blocks are short, and if you don't jaywalk it would take forever to walk up/downtown.

And if you were to fully split pedestrian and vehicle phases (and get New Yorkers to start adhering to it), you'd just grind the city to a halt because you're moving less people/cars than the "maximum throughput" flows than we have now.