I struggle to grasp the concept of one minimum wage for the whole country and honestly, even for an entire state it doesn't make sense. I don't feel Federal Income Tax rates make sense either. I live in a LCOL area and right at the top of the 12% tax bracket. My job in a nearby HCOL area would put me well into the 22% tax bracket (not to mention, much smaller living quarters, higher property taxes, and lower quality schools).
Making sweeping federal policies based on averages or medians does not make sense. Federal government should only be focused on policy where there are economies of scale to be gained. Defense, transportation, education, healthcare, etc.