It's certainly taught but the practical reality is that a lot of people are very sloppy and careless in driving. As a frequent pedestrian in big cities that do allow right-on-red it's extremely common to see cars that try to make a quick right turn immediately at the same moment that a pedestrian crosswalk "Walk" sign comes on, risking running over a pedestrian. When the reality and law is that the car has to wait for the pedestrians to cross and then make its right on red after they have cleared the intersection.

I think the main reason why right on red is banned in NYC is for pedestrian safety and traffic flow reasons.