That would happen if there's no pay cut. Why would I live in NYC, Hong Kong or London if I can get the same salary and live like a king in a cheaper country?
The pay cut will not apply to people working remotely in an expensive city (at least it doesn't in my company)
What makes you so sure that would happen? Many people like the city and have friends & family there. And for the company it makes zero difference if you work from some small town in Mississippi instead of NYC.
The pay cut will not apply to people working remotely in an expensive city (at least it doesn't in my company)