I don't live in the Bay area, but I live in DC and still pay a lot for housing by national standards, and at least for me, looking at it in terms of land and square footage misses the point. Obviously people optimizing for those things won't live in SF or DC (or Manhattan or Boston, etc.). Those things will clearly be more cheaply attainable in places where land is plentiful. You pay to live in a dense urban area because you value the amenities of the city, the economic opportunities it affords, the walkable or bikable lifestyle it facilitates, etc.

My commute is ten minutes on a bike, I live alone so I don't need a big house, and I have no use for a lawn. Your values are clearly different, so New Hampshire is the right call for you (or NC, or whatever). But they're not apples-to-apples comparisons.