Federal government workers in the US generally have a “base salary,” which stays the same across all regions, so you can easily compare. And then they get a regional adjustment, based on where they actually live, called “locality pay.” I think this is recalculated annually based on the specific areas. It’s almost certainly more complicated than that, but I think that’s the gist.

I agree with you, and my point is that the US government already does this! So if it’s fine for government workers, just apply that same algorithm to a federal minimum wage, peg it with some inflation index, and we’ve solved made the minimum wage issue a whole lot better, so we can focus on other issues that don’t have huge supermajorities of support.