If you want your comparison to be equally valid wherever you make it, you have to use the same basket of goods everywhere you go. Otherwise, I can't tell whether you are comparing apples to oranges or pears to grapefruit.
When I look at the numbers for that basket of goods that I currently consume, and price it out for San Francisco, I find that it is completely unattainable for anything less than 3 times what I currently pay, and could be difficult to reliably source for less than a multiple of 4. That's the fact.
It does not matter that I would in reality have to substitute down to inferior goods. It would still be objectively worse than what I have now. The value of my willingness to substitute counterbalances the savings I make by substituting. If I move back to the cheaper area, I won't keep the SV basket; I will substitute right back to the best goods that I can afford.
I agree that there's a big transparency benefit to using the same basket everywhere, but I don't think that actually gives the most realistic answer.
Imagine that every day, for every meal, you eat spaghetti carbonara. You'd be almost as happy eating linguine with pesto, but you happen to have a slight preference for spaghetti carbonara. Now you move somewhere else where, for whatever reason, spaghetti is 100x the price and every other ingredient is only 2x the price. Are you suddenly 100x poorer? No, much nearer 2x, because you'll just switch from spaghetti to linguine. You'll be slightly worse off than 2x because, darn it, you preferred spaghetti, but only slightly.
Moving to San Francisco from (say) Minnesota is a bit like that. Housing is a bajillion times more expensive, so you'll have to make do with a lot less of it, but unless housing is the only thing you care about that doesn't mean you're a bajillion times worse off. You do need some housing, and many other things are also more expensive, so there's no argument that you're worse off in SF for any given level of income. But not by the factor the price of housing would suggest.
(A couple of other remarks about this sort of comparison. 1. The richer you are, the less these things matter -- if you're putting a substantial fraction of your income into investments, those don't change in price at all just because you move to San Francisco. 2. Relatedly, if you are able to buy a house rather than renting, you're not as much worse off as the eyewatering price of the house would suggest -- because later on you can move out of San Francisco, sell that house, and get the money back again.)
Realism takes a back seat to practicality here. A CoL calculator takes two cities and a dollar amount as inputs. A QoL calculator would need a lengthy list of preferences with reasonably accurate price estimates, and a complex network of likely substitutions. That seems like an academic project for a graduate student in economics, whereas CoL calculators are just a simple HTML form with a tiny bit of script and a database of scale factors for each city.
Thus, you can't really tell me how much I'd have to earn to be equally happy in SV as I am elsewhere, but you can easily tell me how much I'd need to maintain equal consumption there.
You can get some of your money back when reselling the house, possibly even within six months of listing it. I would not blithely make assumptions about any market when a bubble appears to be growing nearby.
I obviously felt my comment was already too long and wouldn't on balance benefit from a cautious parenthesis to the effect that you might actually get a lot more money back than you put in, or a lot less, depending on exactly what the housing market does, and that it also depends a lot on how much of the house you own (the limiting case of a 100% mortgage is, at least to begin with, almost indistinguishable from renting), but that to first order, assuming a reasonable amount of equity and no catastrophic shocks to the housing market, what you get out is at least a fair fraction of what you put in ... but as two people have commented on that omission, perhaps I was mistaken.
(As it happens, I indeed didn't own a house in the US 5-6 years ago, but I'm well aware of what happened.)
Yes, but using the same basket of goods is fundamentally flawed because people shift their consumption choices dependent on relative prices. People do not pick the same consumption bundles wherever they go. Your substitution to an inferior good (actually, just less consumption of a normal good, housing space) is compensated with a larger consumption of 'other goods', which have also rose in price but not nearly to the extent your salary went up (tripled, in his previous example). Again, income effect vs substitution effect.
When I look at the numbers for that basket of goods that I currently consume, and price it out for San Francisco, I find that it is completely unattainable for anything less than 3 times what I currently pay, and could be difficult to reliably source for less than a multiple of 4. That's the fact.
It does not matter that I would in reality have to substitute down to inferior goods. It would still be objectively worse than what I have now. The value of my willingness to substitute counterbalances the savings I make by substituting. If I move back to the cheaper area, I won't keep the SV basket; I will substitute right back to the best goods that I can afford.