One of my little pet theories is that civilization (however you define it) advances at a rate proportional to the interconnectedness of humanity. I generally take "civilization" to include things like health, technology, art, engineering achievements, and that sort of thing. "Interconnectedness" is a little more abstract; in my mind, it increases due to technological inventions like spoken language, written language, the telephone, satellite communications, and the internet. These innovations serve to increase what I call the functional population density -- that is, the more functionally dense a society is, the more interconnected it is, and the faster its civilization will advance. SDB has a neat essay on the four most important inventions in history, and I generally agree with his analysis, since it fits so neatly into my own theory. (I'll explain my theory in more detail in a later post.)
Of course, if functional density is good, why, actual density must be even better! Check out this Wired article and read about the future of civilization!
By expanding our cities underground, we will be able to reach population densities unheard of throughout history. Functional density increase due to increased population density creates some difficulties that technological advancement does not (such as crime, waste disposal, heat (you've got to have huge air conditioners for cities a mile below ground), dealing with natural disasters), but I believe that they can all be overcome. Inevitably, there is some equilibrium point where the benefits to civilization and the costs of maintaining a given population density balance out, but we certainly haven't reached that point yet with our current population density-increasing technology of choice: skyscrapers. Major cities continue to drain people from rural areas, and even the largest and most dense cities are still growing (see here).
Now, as to Los Angeles... I don't know how safe it would be to dig here, considering that we can't even build a subway without plowing into tar and natural gas. Oh, and earthquakes. Better than Balrogs, I suppose.