You're employed with a salary of $X at location Y.
Your employer wants you to move to location Z with higher cost-of-living. You can either stay at location Y or move to location Z. You feel it's right that your employer increase your salary because of the higher cost of living if you move to Z.
The company is asking you to make a concession: do the same work, but in a different location.
When you ask to move to a lower-cost area, aren't you asking for the same concession? Why is that concession expected to be gratuitous vs the same concession from the company which is expected to be compensated?