Neither the Northridge quake (1994) or the Loma Prieta quake (1989)resulted in the doomsday scenario you envision. The largest quake to hit an US urban area, the 1906 San Francisco quake (somewhere around a 7.8) was a bit different. Martial law was declared and the army shot roughly 500 looters, some of whom may have been legitimate owners salvaging their own property. Refugee camps were established, including some temporary structures that resemble Katrina cottages, and remained in use for about two years. The 1906 quake was the largest insurance payout in US history until Katrina.

Some looting is an inevitable result of almost any incident, but it takes a really big event to trigger chaos. Historically, California does a pretty decent job of weathering catastrophes. San Francisco in 1906 had a population of just slightly over 400,000, so the next Richter 8 may have a much nastier effect on highly urbanized and heavily populated SoCAl. Maybe we will find out and maybe we won't.