That explains variations in the case of people having to show up daily at the office in some location. The market is that location and you have to pay a rate expected in that area / market.

But in the case of remote, isn't the market the whole area to which you're open? If a company is open to hiring from the entire US, the market becomes the whole country. So if you decide on hiring engineer E, why would you pay more if E decides to live in SF instead of [low COL city]? E is the same exact person and whatever work they do is not dependent on where they happen to be.

The only variation I could see as "fair" would be dependent on how taxation varies. I'm not familiar with how these things work in the US, but if there's variation in payroll or income tax due to the state where the employee actually works, I can understand that for a given cost the company, the employee's after tax salary may vary.