Why would this apply to remote workers but not local workers? Are you saying that you should pay convenience store workers the same everywhere, in New York and Lincoln, NE?
You could turn it around, and I’d say that if rent goes up, wages should go up too. People should get CoL adjustments separately from raises. If we get CoL adjustments for inflation over time (you get paid more in 2020 because 2020 is more expensive than 1990) why wouldn’t it also apply to location (you get paid more in NYC because NYC is more expensive than Lincoln, NE).
(I’d also argue that the value & quality of local workers in dense cities is higher.)