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I think you're missing the point with Bloomberg. The whole idea with that place is that they don't like offices: they don't want anyone to have one because they think offices are a bad thing . They think people work better in one big giant, open, noisy room. A bunch of companies these days have bought into this philosophy, and a bunch of young hipsters think it's great. So Blooomberg hasn't eliminated offices to try…
I agree with your description of Bloomberg's beliefs and motivation for it, and I agree that many other organizations, especially start-ups, cargo cult on the back of this. Since the belief that offices are bad in terms of cost or productivity (e.g. Bloomberg's belief that people work better in noisy, open spaces) is demonstrably and quantitatively incorrect, and inflicts undeniable mental and physical health problem…
For one example of a work environment where noisy, open spaces seem to work well, just look at stock traders at NYSE on the trading floor. That whole environment works by people being close to each other and able to turn around and talk to each other at a moment's notice. I sure as hell wouldn't want to work there, but there are people who seem to like that environment.
I don't like open-plan offices either, but I'm not going to assume that what works for me works for everyone else. From what I've seen, the type of people getting involved in programming in recent years are not the same type of people who got involved in it back in the 70s and 80s, so it's quite possible these offices really do improve productivity overall. It's also possible that certain personality types gravitate toward certain industries, so certain workplaces work better in those industries than in others. The people interested in finance are probably not the same kind of people interested in, say, programming Arduinos. Maybe Bloomberg's office really does work out well for them. I don't have any data to disprove their beliefs, other than my own personal bias, but I can't claim to speak for all programmers.