Much of my extended family is from the Bay Area, mostly circa the North end of the Golden Gate Bridge. My experience is that food
is meaningfully more expensive in the Bay Area, whether eating out or eating in.
Transport does cost me more. I estimate my vehicle's ongoing TCO amounts to ~$250/month (purchase, registration, gas, repairs, insurance, etc.). (It's also worth noting that having a lower monthly TCO for a vehicle than me is possible. The math on an acquaintance's used vehicle brings TCO to ~ $150/month barring major repairs, with him driving more than me.) And of course if you have a fancier car it's more expensive.
So far as "housing costs" go, my total home costs (homeowners insurance, utilities, property taxes, internet, etc.) are less than half yours even treating my mortgage payment/home equity as a total loss. Which is to say cost of living is drastically more expensive in the Bay Area.
But more pertinent to your comment, car ownership is not cheap, but the difference in housing costs between SF and elsewhere is massively more than the cost of operating a vehicle.
Likewise, if I wanted a 2 Bed/ 2 Bath place like mine or a similar flat in SF, I think it'd be more like $4k/month.
So while I do agree it's possible to live in SF for maybe less than you'd expect, it's still very expensive.
That last time I did the math on it, supposedly ~$85k where I am in Arizona was about equivalent to ~$120k in the SF Bay Area, but the SF Bay Area seemed like it'd have lower quality of life. (Though maybe going carless would help more than I think with QoL.) And in general there's sort of a pattern, where at every pay level SF Bay Area has to increase pay by more to match elsewhere for less.