Take another look at this [1] BART map with corresponding home prices for each stop. Yeah, it's cheaper to live outside of the city, but it's still crazy expensive. The median sale price for a house in Pittsburg is $430,000, with a 62 min commute into SF. If you live 62 minutes outside of say, Pittsburgh PA, you can certainly expect your median home will cost ~$120,000 or less [2].
It's been my experience that while square footage cost may go down outside the city, you really end up paying around the same rent for a larger space. So if you can't afford a $3000/mo rent in the city, you probably still can't afford the $2800/mo rent you'll pay in Daly City.
I expect what would really happen if SF just went all in building new housing, is that prices would drop in the city slightly, allowing people to move back into the city, thus increasing demand and increasing prices back to where they were. The places where rent would drop are the suburbs, where people were pushed out to initially.
A way to look at it would be that SF's sphere of rent influence would end up shrinking, but the magnitude of the epicenter remains unaffected.
[1] - http://www.estately.com/bay-area-home-affordability-transit-... [2] - http://files.zillowstatic.com/research/public/realestate/ZHV...