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Are you under the impression that air traffic controllers only work at towers in commercial airports?
Your math is based on incorrect assumptions -- the well-documented ATC shortage actually exists.
The problem is that you're comparing numbers from before Trump's presidency, but the understaffing of FAA ATCs goes all the way back to when the Reagan administration fired all ATCs to break up the union and forbade the FAA from rehiring any former union members.
The FAA has been playing catch up with training enough ATCs to meet demand ever since, which isn't helped by a sequence of bad decisions made regarding ATC training schools.
New York State is large. It has lots of airports [0] - although not all of those are towered, you're still dividing that 260 down by quite a lot. And I don't believe it's standard practice to fly some dude in Buffalo down to NYC to cover a shift. There's a huge staffing problem in ATC right now.
That staffing problem mostly comes down to it being demanding work that's poorly compensated for the amount of skill and education and stress involved; there are high hiring standards, you can't work past 56, and you can't even get started if you're past 31. If you're interested in aviation, you can make far more money as a pilot and it's a much more pleasant job; why would anyone become an ATC?
[0] https://en.wikipedia.org/wiki/List_of_airports_in_New_York_(...