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You're missing one other consideration: retirement savings.

If you have a 401(k) plan, you can contribute up to $17,500 of your salary each year as an elective deferral. While it's possible to come out ahead earning a lower salary in a lower cost of living area, for most folks, it's generally going to be easier to set aside the $17,500/year for retirement with a higher salary. If you have a decent employer match, a higher salary can also be meaningful over time.

Of course, it is possible to obtain the best of both worlds (make a lot of money in a low cost of living area). You don't need to be in a high cost of living area to own a profitable business or become a consultant, and folks who are self-employed can set up their own 401(k)s.