I believe that the benefit of my choice to live in a low-cost area should accrue to me. If the company really believes in a remote workforce, they should pay based on value to the company. I am also saving the company on rent and probably some office-only benefits.

In general, they pay the high-cost-of-living person more because they won't take the job otherwise -- you could also not take the job otherwise.

You will have a harder time finding this, and it's a lot easier if you have the skills to back it up. You have to be as productive as an in-office employee and constantly make sure that is understood.