That's a saving of $30k/year, or maybe $40k/year before tax.
From what I understand from reading comments here, salaries in places with lower cost of living are not just $40k/year less, but much much less.
And for those earning more than $150k, the math works out even more in favour of the Bay Area, as the % drop in salary goes up with salary, whereas the $40k rent difference doesn't.
If you don't mind living in a rented room or commuting >1hr a day and shop exclusively at amazon and costco, the bay area is a great opportunity to save money.
If you're a software your aim is to buy a decent home in $US_CITY at some point, the easiest way to come up with large downpayment is to work in the Bay Area for a few years. You don't have to live in the Bay Area forever.
https://sfbay.craigslist.org/pen/apa/d/old-mountain-view/667...
https://sfbay.craigslist.org/pen/apa/d/pet-friendly-house-nr...
Sounds good enough to start a family to me.
And of course, once you become a little bit more senior and your salary goes over $200K, you won't mind spending so much on rent and will start saving significantly more than elsewhere.
It's possible that there is a natural filter in play here, with the people whose salary is not increasing significantly basically forced to leave.
In your 150k example you're using 1/3rd of your salary just for rent (assuming you get 150k, net).
[1] https://www.rentcafe.com/average-rent-market-trends/us/ca/sa...