No, Beverley Hills is desirable specifically for its prestige.
San Francisco is desirable as location convenient to jobs and transportation.
Not having more housing in Beverley Hills has no real impact on the rest of LA. Not having more housing in San Francisco means the extra demand spills over into a variety of other places.
Higher Density housing does not necessarily result in a location being less-nice. Vancouver BC has made a point of choosing trading density over suburban sprawl with supposedly nice results:
San Francisco is desirable as location convenient to jobs and transportation.
Not having more housing in Beverley Hills has no real impact on the rest of LA. Not having more housing in San Francisco means the extra demand spills over into a variety of other places.
Higher Density housing does not necessarily result in a location being less-nice. Vancouver BC has made a point of choosing trading density over suburban sprawl with supposedly nice results:
http://en.wikipedia.org/wiki/Vancouver#Cityscape