There's a vast difference between what is taught and what is actually done. Everyone (well almost everyone) knows what they are supposed to do as drivers, but few do it.

It's taught and the law.

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.

I imagine the insane traffic volume in NYC also incentivizes more aggressive driving. There's a higher trip time penalty for not making the turn, compared to a city with less jammed roads. This matters for people who need to make appointments or any other driving where time matters (does anyone still offer pizza delivery in 30 minutes or it's free?).

I live in Boise, Idaho. I can confidently say that the behavior described is not unique to NYC scale. I don't have the context to say it's not worse there, but I can confidently say that license plates coming from more rural counties don't appear any less aggressive or careless than local plates.

In many places a pedestrian is a rare sight and drivers forget they exist.

Taught? Of course. Do it? lol.

America is the land of "the rules are all there for someone else to follow."

See how we feel about genocide, presently.