Governments also do this with overseas postings. Depending on where you are assigned, you will get an adjustment.
I agree with @LuFins-Dad , in theory, it can be a good idea to have different minimum wages.
Of course, then you would have people on the border line complaining that they cannot hire anybody, because they will just go across the minimum wage "border" and get a job that pays more.
Not sure how it would be set up, but in theory, I think it is a good idea.