Consider a typical median priced home of $540,000, with a typical size of +/- 2000 s.f.

probably in the range of $50 to $70 per s.f. of living area

So for 590K-610k I can get a 3000s.f. home in those areas? Hmmm.

Medians, in general, don’t carry a lot of information. You don’t even need math, just rank order. There are a lot of factors that can skew the median, as you have mentioned. Do you really believe that they skew in a consistent way (and then at best we have a skewed, yet consistent measure) or that the measures mentioned are orthogonal such that the factors that skew the measure are independant and cancel each other out, leaving a robust measure of resale prices? I find the second to be harder to justify.

None of this rejects the hypothesis that this may be the best measure available to the general public. Banks, capital markets, risk managers with millions of dollars in play, eh, not so much.