I strongly endorse this. I'd argue that it's totally compatible with expanded housing, though.
The population density of Somerville, MA is 18,000 per square mile. It's the 16th densest municipality in America, only narrowly behind San Francisco itself (18,600). That's almost 3 times Berkeley, CA (6,400), and 7.5 times Palo Alto, CA (2,400).
Somerville is also a pleasant, human-friendly city devoid of skyscrapers. It's a perfect example of mixed-use urbanism. The tallest buildings are ~12 stories, and that's government housing on the edge of town - almost everything is far shorter. That's nuts - it says we can massively increase population density while maintaining a Strong Towns approach to urban design.
Somerville cheats a little bit, because so many residents work or go to school in Cambridge and Boston. (Workplaces obviously kill density, since they're sized per-person but exist parallel to residences.)
But Somerville's real advantage is being old - older than stupid zoning laws. There are only 22 residences in all of Somerville that would be legal to build today, despite those old, illegal residences being livable and massively in-demand.
http://cityobservatory.org/the-illegal-city-of-somerville/
I don't think there's really a dichotomy between "live in NYC/SF style skyscrapers" and "overpriced housing with urban sprawl". You can relax zoning restrictions without getting highrises and tenements. It just requires careful planning and a willingness to abandon suburban, parking-lot filled design.
A good summary of the bad effects of urban sprawl is available on Wikipedia [1].
2) The more affordable places tend to have less economic opportunity (which is part of why they're in lower demand and more affordable in the first place), so moving there isn't necessarily a win.
-edit
So I see a few comments discussing things like commuting, urban sprawl, etc.... Those are fair comments and I largely agree. But the solution proposed is not the right answer either. We need mixed-use developed walkable neighborhoods. We need our work places to be mixed within our neighborhoods along with our parks, convenience stores, and everything in between. Obviously I'm not a fan of sprawl, but I'm not a big fan of skyscrapers, and I'm also not a fan of others being upset about the affordability of the world's most desirable areas. While it is true that there is much more economic opportunity in a place like San Francisco than, say, middle-of-nowhere Arizona or something, it would be incorrect to suggest that there is no economic opportunity. Frankly, the assessment being made here is that you're choosing to suffer a 2-hour each-way commute and unaffordable rent for the opportunity to work at really cool companies, but the solution, which is to force other people to change their way of life, even if you find it contemptable, is an inherently immoral stance. If a town votes in a mayor who does what the town wants, what is more American, and democratic than that? Is overrunning the town with lawsuits and fights an ethical thing to do? I don't think so. Pack your stuff, and move. When (insert company here) can't get employees to relocate to the insanity that is the Bay Area, they'll move their offices, and things will resolve naturally and peacefully.
Disclaimer: I have never lived long-term in the Bay Area and I have no vested interest in how any of this turns out. If anything, reading the horror stories about people subletting camping spots in their backyard and the like amuses me (obviously I feel bad too). I do confess I have a vested interest in promoting mixed-use development neighborhoods and I would like to see more people move out of the Bay Area and back into the rest of the United States as I believe that the concentration of wealth and knowledge in one (or a few) areas is contributing to the fractures in our society and anti-competitiveness of our second and third-tier cities.