If you were to keep it as a purely economic exercise then it makes difficult to actually justify moving to SF unless your net salary increase actually covers the COL increase.
A few things to keep in mind about SF is property taxes are locked and do not go up significantly due to Proposition 13*. So that is one reason property prices are higher in general the carry cost of the house is cheaper than in other states. Also factor in that on average property increases in markets like SF and NY outpace other regional markets.
You can make the numbers work out if you do not keep the same square footage as your current place. There a few thread here that give examples of how to control cost living even in places like SF and NY. You just have to be creative.
In my example I moved out of a two bedroom 1000sf apartment in a suburb of NJ to a 600sf one bed room in SF for $150 more. But our quality of life is significantly better because the city suits our lifestyle more. We don't drive as much, we are more active, we get to enjoy free activities, instead of always going to a mall, movie or restaurant in NJ. We put 5,000 miles on our car a year vs 15K in NJ.
I didn't even get a significant salary increase, but my work life balance improved significantly. I didn't have to deal with commuting to NYC which can suck up 2 hours from NJ. I also don't have be in the office 9 hours a day even if I get all my work done. I can leave early and work from home 2-3 days a week at most companies in SF because that's how everyone is used to working. So on an hourly basis I increased my salary by about 50% because I just don't have to put in so much time 'working'.
However in your scenario, it would be hard giving up 200k of savings a year which is buying you 4 years of freedom for every one year of work. I would ride that gravy train until you can supplement the COL increase with your investment gains. At a certain point the additional 200k just mean less and less to you, I would assume, as you reach your FIRE number.
*
https://en.wikipedia.org/wiki/California_Proposition_13_(1978)