I'm surprised so many people are so angry about the pay cut. Using my company's simulator, the pay cut seems to be at most 15% of the base salary and most likely less than that. In my case, considering cost of living, it would certainly be most advantageous to work remotely. I would save more money and live in a much nicer place.
I think that's because many people think (rightly so, IMHO) that this is just exploitation by companies that sense they can squeeze a bit more out of employees because employees will likely accept (partly for the reason you mention).