Your math is right. But, you've got to understand the cost of real estate is much much more than double in SF. Realistically, in Ralleigh regional area you can pay 120$/sq ft vs 1000$/sq ft in the SF Regional area (perhaps 500$/sq ft if your willing to commute for 3 hrs/day).
Now, SF might be a great place if you have no kids, no expenses and rent a tiny little room. But, as soon as you want to have a family and backyard, you better get out! SF and CA in general is no place to raise a family. The key in this strategy is, don't put down roots in the CA bay area.
I live in SF, I understand the cost of real estate. I'm not arguing that lifestyle expectations are very different between cities. So given you move to SF and understand you'll be in a smaller house because that is the market norm, the COLA still is only on what you spend.
Now, SF might be a great place if you have no kids, no expenses and rent a tiny little room. But, as soon as you want to have a family and backyard, you better get out! SF and CA in general is no place to raise a family. The key in this strategy is, don't put down roots in the CA bay area.