"If I worked remotely for Facebook and wanted to move somewhere central where rents are three times higher, would Zuck give me a raise? Somehow I doubt it."

I can't speak for Zuck, but Sundar does. I work for Google. We also have local market indexed compensation (which I support, but not relevant to this point). If you move to a city with higher labor prices, you get paid more. I've seen it multiple times with people in my team. It's a total non issue, just paperwork. Very very standard.