This assumes there is no elasticity to where people live. For many people there is a cost at which moving to a higher COL area for an adjusted salary makes sense. Or in general someone may be looking to move for the right job at the right price, etc.
>Cost of living tends to follow from the prevailing wages in the area, not the other way around.
I tend to agree with this, but I think there is also a dichotomy of destination cities (where people with lots of money move to because it's nice, not necessarily because they will make more money there) vs. non-destination cities which can distort prices absent of wages. See: Vancouver, parts of LA, parts of the NY area, Miami, etc.