You would be surprised how many NYC apartment/co-op/condo buildings do not permit laundry appliances and or even dishwashers.
Problems lie on several fronts:
One, as previously discussed, electrical wiring. Though that may only be a problem when using 220v appliances.
Next, one must remember NYC has some of the oldest housing stock in the country, this includes many of the highly desired brownstone and pre-war buildings. Plumbing simply cannot handle all that drain water from washing machines. Maybe one person's might get away with it, but not a majority of the building.
Remember also apartment buildings in NYC are not metered for the most part. That means either landlords or the building as whole pays the water bill. It wouldn't be fair for those not having laundry appliances subsidise those who do.
Finally there is the problem of what happens if the laundry overflows, who is going to pay for the damages? In co-op/condo buildings that allow laundry appliances, it usually is written somewhere to cover this area, and or the household must carry some sort of insurance.
The above not withstanding, many people do have washing machines and or dryers in their NYC apartments. Both our appliance dealer and repair person will ask customers the common question before making a delivery/repair call "does the building allow washing machines"? If not they will try to disguise the appliance(s) in another box, and or for making service calls, say they are there for another reason. Sometimes this works, sometimes not. Our appliance dealer says more than once delivery people will be stopped and asked to open a box to show the building service people/landlord what is inside.
Oh yes, the final problem is that NYC has one of the largest population of nosey and or whinging people on the planet. If that washing machine or dryer annoys your neighboor(and for some that does not take much), plan on hearing from your building/landlord the next day.
L.