No city on Earth is full. (Indeed, estimates of human population growth show planetary population stabilizing at less than one tenth our global carrying capacity, so this is not surprising.) It would be extraordinary for the Bay Area to be the first, and so calls for extraordinary evidence.
Housing is a cost of living. Driving the cost of being alive as low as possible should be a high priority. We should use the tools we have to do it.
We don't need to pack everyone in like sardines. As you already noted, there's plenty of space in the world. (You just have to turn your eyes outside the peninsula).
P.S. I do not live nor aspire to live in the peninsula, or anywhere near it
No other city is full because at some point people decide not to live so tightly packed together, and demand dries up.
Current laws raise prices to enforce low density. That's wrong.
Personally, I have definitely noticed many people who have convinced themselves they have to stay despite their miserable conditions. Nevermind they have no family in the area, few friends, and despite their very well paying job they can barely afford food & rent. They could surely never be happy elsewhere!
It's like some kind of bubble, where we imagine the whole rest of the country is a backwater hellhole and won't even imagine we could leave.