> Berlin lacks the kind of internal economy to support that kind of situation
Also, in contrast to London and New York, it's not the financial center of the country. That would be Frankfurt-Main.
And the role of a city having three universities, with two others in close proximity (Potsdam and Viadrina) plays a major role.
Back in the day, and long before the introduction of the Bachelor/Master system, pretty much the only students Berlin attracted were explicitly radical leftist ones.
Because there wasn't any pressure to get a degree in four years, one could eke out a comfortable existence for a decade or so by having an official student status, paying student-rate health insurance, benefiting from other reductions in subway fare etc., and generally spend most of one's time on politics. The student demographic has changed in the last decade or so. Most of the Marxists have retired from the OSI at the FU, so it's no longer a mecca for radical students, but rather upper middle-class poseurs from Southern Germany attracted by the Berlin-hype whose wealthy parents subsidize their bohemian fantasies.
Also, unlike a lot of wealthy Western states, Berlin still has no tuition fees, thanks in part to when the PDS (now part of Die Linke) was the junior coalition partner to the SPD government and responded to activist pressure. The fact that wealthy Western/Southern Germans will gladly benefit from a situation like that by sending their kids here to study, while still voting for neo-liberal parties like the CDU/FDP/Greens/SPD, is just another example of arrogant Wessi hypocrisy.
The sheer scarcity of study spots due to increased demand led the Universities to introduce strict admissions requirements based upon grade point average since the mid-2000s, which means for example that a lot of actual residents of Berlin are actually shut out of university spots. Rents go up because the "creative class" decides to stick around after four-year playtime is over.