If you take a pay cut for relocating to a lower CoL area, you are being stolen from.
Then the notion that anyone is being stolen from is just completely ridiculous.
They pay the minimum they feel is required to retain you and prevent you from going to a competitor. And if that amount exceeds the cost to hire someone who can do your job as good as you, they want you gone. That’s it.
They know that working remotely from a place with a lower cost of living is a perk. They know even if you take a pay cut, you’ll come out ahead. They know the minimum they need to pay you to retain you has gone down.
Look at an international circus contract, for example (I was in one). A group of performers from different countries performing in the same place get paid different amounts for doing the same exact role in the show (up to 2.5X difference, by the way) just because the company can get away with it. It's about the cost of the best alternative (for the worker), not about some intrinsic worth of the work.
As for whether you should subsidise someone, if it makes you more money overall then of course you should. Regardless of what luxuries they have.
We should have open pay scales by position with well-defined criteria for bonus / raises. Negotiation should have little to do with it, ideally.
Pure value rarely has to do with your salary; it's more about supply/demand. If we doubled the supply of people doing your exact job right now, your ability to negotiate (and your salary) would probably drop, even though you are delivering the same "value" to the company (unless value encompasses supply & demand).
(As I've mentioned above, I've seen pay differences in circus of 2.5X for performers with different passports doing pretty much the same exact job in the same exact show - the value they were delivering was the same, the only difference was country of origin). So pay is also about cost of best alternative.
The difference in income taxes is paid (or saved) by the employee.
Food, gas, plumbing, etc are also cheaper.
For me at least the added COL is more than offset by the higher pay.
Edit: This is more a pre-Covid comment. No idea the math for remote post-Covid.