This is true in lots of fun cities, primarily because it's so hard to build new housing stock—which is a Bad Thing, as Matthew Yglesias describes in The Rent is Too Damn High. Britain is suffering from a variant of the "no building" problem too: http://www.buzzfeed.com/dlknowles/britains-dysfunctional-pro... : "Construction started on just 107,000 new homes in England last year. Excluding World War II, that’s the lowest figure since the 1920s."
The solution to "gentrification" and what not is "building new dwellings," which we know how to do very effectively (elevators and steel are century-old technologies). The problem is regulatory / political.