If Person A is outperforming Person B, but is getting paid less because they happen to live somewhere else, you lose the ability to claim that you compensate people for performance without sounding like you're talking out of both sides of your mouth. Not only is Person A not going to be happy about that, Person A is not going to believe that compensation at your company is based on performance.
Companies that want to hire and incentivize the best people need to be congruent in their messaging around compensation and performance. Claiming that compensation is performance-based and then including a factor (location) that has no bearing on performance is incongruent and will not help to develop the right culture in this regard.