I'm not convinced this is really true in a lot of the "actually desirable to young tech people" areas of southern cities. I just checked rent prices in Franklin, TN for a contract project opportunity and found newish apartments are going for $1300+. Trendy parts of Raleigh are renting apartments for $1100+. Meanwhile, it's very difficult to live in the South without a car, and salaries are far lower than $24k under a Bay Area tech comp structure (assuming you rent at the $3k level there).

I will grant you that if you have a family it's way cheaper due to availability of real houses in the burbs combined with cheaper daycare/nanny/housekeeping/etc., but a young, successful tech worker is probably better off on the west coast despite the higher cost of living.