This makes no sense.
For employees who are required to work in the office it makes sense to pay more at offices in places with higher costs of living. That's because your pool of potential employees is only people who live there or will move there. The company is requiring that employees live in a specific area so must pay based on the costs of that area.
For full time work from home employees the company has no reason to care where the employee lives (other than regulatory--they might not want employees who live in areas where dealing with taxes or regulations are complex or costly). Hence the company should have one uniform rate for full time work at home employees, high enough so that they can get fill all their openings.
If that means that the rate is too low for people in NYC why should the company care as long as they can get enough people from Stamford and other places with lower costs of living than NYC?