I might be hopelessly naive, but why not do the new growth somewhere else? The BA is pretty obviously "full" already, and adding more housing of any kind isn't going to make it better.
By contrast, NYC has 27,016 people per sq mi; the densest suburb of Boston (Somerville) has 18,431; West Hollywood has 18,297.
There's plenty of room for more people in the Bay Area, if denser housing is allowed.
I believe I looked for something like that in the BA and it doesn't really exist.