Southern California made it through the Depression better than the rest of the country, however, the tremendous population growth of the post-WWII era caused the cities, suburbs and freeways to overrun the golf courses, leading to the demise of a lot of classic designs by Thomas, Bell, Watson, Dunn, Behr and others.
Daniel Wexler covered it well in his two books about defunct courses. Such highly thought-of courses as Fox Hills (36), El Caballero, Royal Palms (actually a Depression victim of the 30s), Sunset Fields (36), Pasadena Golf Club, Midwick, California CC, Inglewood, Flintridge, Lake Norconian, and others were swallowed up in the 40s, 50s and 60s.