Another way I've argued this is whether it would be appropriate to ask an employee what he/she pays in rent and then base their salary on this number. Everyone agrees that is nuts, but cost of living is (as you pointed out) heavily influenced by rent.
The only reason this currently works is because the market hasn't reached a tipping point where there are enough remote opportunities, and I suspect that when it does people will remember which companies did COL based salary.
Now all this said, I do understand a slight adjustment in salary for remote employees vs in office ones in some cases but it should likely be a fixed adjustment regardless of where you live.
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