Compare to LA, where people tend to wait for the signal to cross pretty consistently. That said, LA still has horrible pedestrian death statistics so who knows how much that matters.
LA is generally the opposite -- it's a city for drivers, not for pedestrians. So the norms are different.
Right turns at red lights are illegal in NYC, and most of the streets in the city are one-way, so for a pedestrian to cross the street against a signal with no oncoming traffic is reasonably safe.
To give a more concrete example. Say a traffic light has a pedestrian light attached. It will only allow pedestrian crossings when it does not stop the flow of vehicular traffic (say every 3-5 min, and only for 20 seconds at a time). But it does so regardless of actual traffic (no cars are passing the intersection when many pedestrians arrive), you can’t really blame the pedestrians of ruling this system as stupid and opting not to follow it.
Who says it's a mistake?
It has nothing to do with the signals and everything to do with the pedestrians. If you actually want people to respect the signals, place traffic police on every corner in Manhattan and issue jaywalking tickets to absolutely everyone, for months on end, and you'll see it. (You'll also see a backlash.)
Other than that, it's not happening.
https://www.nytimes.com/1998/01/13/nyregion/with-higher-fine...
(You will notice this idea is unworkable due to excessive manpower requirements. It is undesirable for other reasons as well.)
That's the kind of thinking that makes our roads so deadly. If a rule in particular seems really silly to you, file a complaint / suggest a change so that it takes more parameters into account but until it is changed, stick to it. Loose some seconds or even minutes, I don't really care. These security rules should be followed by everyone, and people with your line of thinking shouldn't be allowed to own a car.
I'm not a fan of cars already, but people driving cars while following safety rules only when it suits them is what make them a lot more deadly imo.
Sure I can, they have a shit culture with little regard for traffic signals. My city has the same problem. I'm the odd man out for waiting for a signal, and am mocked for it at times. Nothing wrong with the signals or timing as a pedestrian (as a cyclist that's another story), but people feel they are more important. That they're 15 - 90 seconds is worth more.
Similarly, had a man recklessly pass me in his vehicle while I was biking to work yesterday. He went fully into the oncoming well above the posted speed limit, and cut me off as I was turning from the forward-moving lane into the left-hand turning lane. All to get around me to a red light.
Some people feel their 15 seconds are more valuable than others safety. In the case of pedestrian jaywalking, that their safety isn't worth the inconvenience of using the nearest crosswalk.
Pedestrians aren't carrying a multi-tonne vehicle that can kill people. Traffic lights are for drivers, and it's drivers who should pay attention.
The first step to fixing traffic deaths is fixing the laws that make causing a traffic accident more affordable than paying attention on the road. Right now you can drive while using a cellphone and run over as many people as you want if your excuse is "they came out of nowhere".
The responsibility of not killing people is on the drivers.
When I first moved there I was annoyed by everyone ignoring the signals. Then I came to appreciate it as an efficient way of getting around the city. Pedestrians (and bikes and cars) all used the signals as general guidelines, but would go when it was safe, because otherwise you're never going to get anywhere.
I'm not saying that everyone everywhere should ignore traffic signals, but it seems to work well in New York City.