San Francisco's population density is 7,000 people per square kilometer. There are many beautiful, beloved cities throughout the world that manage to accommodate far greater density numbers:
Every yellow block in that picture is zoned 40-X, which means that buildings taller than four stories are not welcome. If we raised that to six stories (as is the norm, e.g., throughout most of Paris), we could easily accommodate hundreds of thousands of new residents.
* Barcelona: 16,000
* Buenos Aires: 14,000
* Central London: 13,000
* Manhattan: 25,846
* New York City (overall): 10,100
* Singapore: 7,600
* Paris: 22,000
* Central Tokyo: 14,500
Here's a map of the zoning ceilings throughout San Francisco: http://i.imgur.com/Tn7CSTX.jpg
Every yellow block in that picture is zoned 40-X, which means that buildings taller than four stories are not welcome. If we raised that to six stories (as is the norm, e.g., throughout most of Paris), we could easily accommodate hundreds of thousands of new residents.