NYC's cyclists (of whom I know many) need to follow traffic laws.
Those laws are there because people need to act predictably on the street. When a red light becomes a mere suggestion for cyclists, motorists eventually start treating them as such as well. Monkey see, monkey do.
...and getting t-boned by some douchecanoe driving a car when you have the light is commonly fatal for a cyclist.
There was an uptick in utterly shitty driving from 2019 onwards in NYC, and the police stopped all enforcement actions even in egregious cases... then the roads became, and largely remain, a free-for-all. I've seen some attempts recently to start clearing the mess up, but too often NYPD are ignoring these dangerous road users... or hiding their license plates and being offenders themselves.
...and this is before you're fighting for space in a the bikelane with some drunk+stoned asshole on a moped.
I'm fully in favor of delivery professionals being required to have a license and display it at all times when on the clock. They should also be required to have specific insurance, and a highly visible personal identifier when working. They should also get automatic Union representation and a living wage.
Anything more powerful than a class-C e-bike should have a license plate, and if not it gets taken and destroyed, or auctioned to a more responsible owner. Sales of these vehicles without a registration needs to be illegal.
Anything more powerful than a class-C e-bike found in a bike lane should be impounded on the spot.
Running a stop sign or a red light should get you a ticket, regardless of what wheels you're on.
Going the wrong way down a one way street should get you a ticket.
It doesn't help that NYC doesn't have the space and largely practices "maximum-conflict" street design... but that's just the slow, shitty entropic action of self-serving interests pushing communities around, and they react very slowly. It takes (usually multiple) fatalities for anyone to wake up and actually do anything about it.
The solution for large scale behavioral problems isn't telling loads of people to do better, it's systemic change, and in this case that means infrastructure for safe biking. That includes traffic calming measures, separated and protected bike lanes, regulation to reign in vehicle sizes and weight, etc.
The OP is correct wrt powerful e bikes sharing space with pedestrians and normal bikes.
They are a different beast, heavier and noisier. They have much higher speed limit, and require less effort (some models need no pedal power) to travel. This, alongside the rise of delivery services, encourages people to overspeed (more than 20mph).
15mph is roughly the limit of what makes bicycles safe for mixing with pedestrians, but beyond this speed, they aren't that different from a motorbike in terms of road design considerations.