As someone who lived in South Bay for 5 years, I'd hardly call it a "desirable area".

Sure. Most of that desire is "I want a high paying job". With that goal, they sacrifice things like affordable housing, good schools, crime, congestion, etc.

Don't forget housing is stupid expense in NJ as well. I wouldn't call NJ "desirable".

This is true and explains some of it, but it doesn't change the fact that currently wanting to live in a desirable area and wanting to live in an area because of a job are conflated with no options that could effectively separate or distinguish between the two sources of demand. It's not like everybody would get up and leave the Bay Area, but it would allow those who only want the job to leave the market for housing in the Bay Area and lowering demand overall. At worst, the drop in demand would be supplanted with people who wouldn't move to the Bay Area at the current price (and thus the price wouldn't see much of a drop), but at least you wouldn't be crowded out by people who would leave the Bay Area given the choice.

West coast cities would be my definition of undesirable.