Cost of living can vary considerably even within commuting distance of the company. Would a company pay more to a non-remote employee who lives in an expensive neighborhood than to one who lives in a poor neighborhood? If not, why should they do this for remote employees?

Depends on who you ask. But really, "fair" isn't the question.

The real question is: Will companies do it and will (some) employees accept it? Yes.

If you're a remote employee should you negotiate hard with a company that tries to do this? Yes.