This is far and away not only an SFBA regional issue.
http://www.bizjournals.com/austin/news/2017/02/16/austins-ho...
Our problem with Austin has always been the city council artificially limiting development. We didn't allow 10k sq foot lots until last year which means we're JUST now starting to build those 3-4 story townhouses near downtown. If you go to Dallas or Houston they are all over the place and little neighborhoods will feel vastly more populated than they do in Austin. The unfortunate part of this is that now younger people who could afford these townhouses are pushed into tiny studio apartments downtown or into houses 12-20 miles away from downtown. There was no in between if you didn't have millions to spend but wanted to live in/near downtown like there is in Houston/Dallas currently.
SJ is over 3x the surface area of SF but has barely 20% more residents in that area. Imagine if they just doubled density --you'd allow for the absorption of an extra million residents. If they only upped the density by 50% they'd allow for over an extra 500,000 residents --that would alleviate the issue by itself.
There is so much poorly built stock from the 60s and 70s that it would not only renew the city but it would become the undisputed powerhouse of the bay area.
A housing shortage is trivially easy to recreate; just stop building housing while trying to pack more and more people in the same space. An SFBA-grade housing shortage isn't that much harder then, you just need to convince a small handful of people on city and county boards to stop building housing, while trying to put more people in the same space. Sprinkle some income inequality that makes Rwanda look equitable and you've got a plot of dirt going for $200k in South San Francisco.
You could pack half the Bay Area's population into Santa Clara county if you made it as dense as San Francisco but there's not the will to go even that far, never mind somewhere actually dense. New York's not even all that dense in the scheme of things, but at that level of density, you could fit almost 36 million people into Santa Clara county alone, or the whole Bay Area, and then 3 more of them.
Hundreds of companies being located in the same area isn't the problem, the refusal to build more housing is.
There is no rational reason why Palo Alto should have detached houses with lawns, or Sausalito be a little town, except for terrible political decisions about land use and mass transit.
Secondly, the Bay Area housing shortage is a phenomenon of hundreds of companies being located in the same area. No one company, even Google, could have that same impact on another metro area. You're only going to stand a chance of recreating the SFBA housing shortage (and it's a small chance) if the whole Bay Area market moves wholesale to a single new place.