The question of paying remote employees the same as "regular" employees is complex. Switching to the hypothetical:
If a company is headquartered in Louisville, KY, and somebody wants to work from e.g. Los Angeles, it would be ludicrous for the remote employee to accept the same salary in LA as in Louisville because the cost of living is much higher in LA. Considering the opposite situation, I find it unlikely that a company headquartered in LA is going to jump at the chance to pay an LA salary to somebody in Louisville.