I wanted to add: If you live in SF and make $150k/yr and are able to put away 10% on investments that's $15k/yr. If you work somewhere else and take a move and make $75k/yr and are able to invest 20%, you haven't made a financial change. But a pay cut that big likely means you're somewhere that has less going on, less access to food, less for different types of activities, lower quality schools (that are funded less because property tax is lower), lower quality hospitals (big cities can afford all the fancy equipment and big time doctors), etc.
So to be honest, moving to a cheaper area with the exact same COL might not be better because of other factors involved.
Price, as it turns out, is a signal of value. Some of the value might be access to jobs which you may now be able to access from elsewhere, but certainly not all of it.
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?
So to be honest, moving to a cheaper area with the exact same COL might not be better because of other factors involved.