Yeah people always miss this: Job availability is not the only reason people don't all move to rural Kentucky. People like living in expensive cities! That's why so many people live there!
Not that they'd do this, but if the company offered what it was paying for office space for you as a stipend for your home office, would that change your mind? Some quick Google math suggests an average of $80/sqft/year for NYC office space and suggests 100 sqft per-person for an open-office worker which comes out to $600-700 a month. Again, cursory Google search, but it looks like that's right about the price increase to go from a 2BR to a 3BR and have a home office.