Even for remote workers sometimes there are differences depending on location
Lots of variation, but the variation is at the employee's discretion. It's not the employer's job to compensate unless the location is of benefit to the employer.
It would be no different than paying employee's more based on the car that they choose to drive. Buy a Mercedes, we give you a raise. Buy a Toyota, your pay stays normal. Be responsible and take public transportation and get a pay cut to add to your woes.
Basically, employer's rewarding unnecessary spending is an insane business tactic. It's not just bad financially, but generally punishes good decision making. An employee living in low cost cities or even villages are likely dealing with fewer business-interrupting problems than employees in big, expensive downtowns.
What I've been told is that it goes by local market... based on the cost of labor in a given location, remote or not.