While that's true, the calculator presented isn't as bad as you make it out to be. It splits up the calculations across several different indexes. Food, Housing, Utilities, Transportation, Health, and Misc.
It's increase is based merely on the average. This is probably fair, considering if you want to maintain the same life style you have in one location, this gives you an estimate as to what you'll need. And I imagine if you live in Detroit and spend a substantial portion of that on housing, you'll need that much of a pay raise to maintain that same level of housing. You even suggest this: "The one kicker will be housing--you'll probably need to settle for a smaller living space."
That's the point. The monetary comparison assumes you maintain the same level of housing. Obviously it's not precise. However, if you accept that housing will be different, you can remove it from the equation. In this case, the overall percentage is used, but housing is the reason for that. Remove housing, and it helps get a good idea of overall living costs.