It's the stations that are under the street, mostly in Manhattan. They have narrow channels on either side for stairs, and all the other space is filled with building foundations, actual buildings themselves, and other ancient infrastructure.
They can't replace an existing stairwell with an elevator, since:
Severe fire code problems due to loss of egress in already extremely crowded stations (there's nowhere else to add a new stairwell)
There isn't a full vertical channel anywhere that can access the station: angled stairwells and tunnels provide all current access
Direct platform elevators are literally impossible because they would put the elevator in the middle of the street.
Those old stations are often separate for uptown and downtown, so even if you can solve these problems for one platform, you have to do double the work for the second platform.
The stations affected by this are tiny and sit in the middle of a ton of existing infrastructure. Short of eminent domain and removing existing buildings, there just isn't anywhere to put an elevator.
Uptown, there's the opposite problem. There are stations so deep that stairs are considered too dangerous from a fire code perspective: they're elevator only. But, the extremely high throughput of those stations now means that the elevators can't clear the platform as fast as arriving trains fill it sometimes Elevators (especially the pneumatic ones that need to be used in these situations) can't give enough throughput.
I believe all of the major hub stations can be made compliant: cost is the sole limiting factor. Same goes for most of the stations outside of Manhattan. It's the ancient Manhattan ones that are intractable problems They're barely fire-code safe as it is, with a small number of long, twisting stairwells providing sole access. They'd be shut down in any other city, but they're too important to the daily commute to do so despite the danger.
I really want to see that lawsuit force faster progress. The stations I'm talking about are only a quarter of the system, so even if you ignore them, there are still a couple hundred stations that COULD have elevators but don't for no reason but budget.
I do, however, take umbrage with the comparisons to other mass transit systems. It ignores the inaccessibility of all the cities that don't have any usable mass transit to speak of. It also compares the biggest mass transit system in America to MUCH smaller systems. DC has less than 100 stations, mostly built in modern times, and less than 1/5 the ridership of the NYC subway. The DC system also provides far fewer service hours and much lower train throughput.
It can shut down entire lines at night and on weekends for maintenance. Meanwhile, New York is shutting down ONE line for hurricane-related repairs, and it's projected to cause shocking economic damage affecting millions of people.