Being on the periphery of a high cost area is probably the best deal. For most companies, for example, I imagine that Boston/Cambridge will be considered the same as Boston suburbs--even though within an hour drive you can get to vastly cheaper housing than in the city proper.
So to be honest, moving to a cheaper area with the exact same COL might not be better because of other factors involved.
How many places in the United States have the immigrant communities of the Bay Area, for example? And how do you recreate such communities in cheap places without making them expensive?
Only if you don't live frugally, or if you aren't a senior engineer.
If you do, a lot of the high costs of a high-CoL area can be avoided.
If you are a senior engineer, that XY% raise over a junior is free money... Applied to a larger starting salary.
Oddly enough, high-CoL areas have the same, or higher % raises, when you are promoted, than low-CoL areas. In the mid-west, the wage difference between a senior and a junior may be $30,000. In the bay area, it can be $150,000. Your CoL doesn't go up just because you have a better job title.
So you can own/lease a broom closet or pied-a-terre in Expensiveton, maybe rent it out intermittently or to a "roommate", and actually work and sleep in Cheapsville.
If home address has an impact on take-home pay, it will be gamed just as hard as all the other metrics.
Does relocating from San Francisco to San Jose also come with a pay cut? What about to Stockton? Modesto? Further out?