The type of housing you can afford is a quality of life issue as much or more than it is a cost of living issue. If you live in San Francisco or New York, you accept a smaller living space than you'd get elsewhere. In return, you get access to nightlife, concert venues, and other amenities that can only be had in a densely-populated area.
If living on a hundred acres of woodland is important to you, you will not live in San Francisco. If being able to bike to work is important to you, you will not live in Los Angeles. If staying out of the cold is important to you, you will not live in Minneapolis. Money won't buy you any of these things.
At some levels, it may seem that it's just an issue of money. You can, of course, buy a detached, single-family house in San Francisco. It'll cost you millions, but you can do it if you're rich enough. Attempting to paint this as a difference in cost of living, however, is simply disingenuous--the detached home in San Francisco is the local equivalent of a mansion in my home town. It's not equivalent, any more than hiring Michael Franti to make a personal trip out to Connecticut to play for you would be equivalent to catching a show at a local concert hall.
And, finally, it's important to remember that unless you're living entirely hand-to-mouth, not all of your income goes to living expenses. If you're in the well-paid engineer club, then hopefully only a relatively small portion of your income goes to living expenses. Moving from a cheap location to an expensive one may increase that portion, but it doesn't make any sense at all to multiply your current income by a constant factor to determine the "equivalent" in a different location. That's what that calculator does, and it's deceptive and wrong.