Have you heard of Holocracy? It's one of the more popular of set of flat, self-organizing management structures; it's been tried at a few big name companies, with limited success. I think failures at this point are easily attributed to sheer novelty and lack of experience, and good guidelines for avoiding pitfalls, more than a fundamental flaw in the concept. One of the big issues I see needing to be addressed is ego; we will never get rid of self-proclaimed alpha types, and extroverts will always have an advantage in rising in the ranks regardless of competency. These sorts of issues can sabotage - even without malicious intent! - these flat structures. Some people will simply tend to accrue influence and power. But another issue is overcoming the tendency to bikeshed. Companies who've tried, and failed, to execute Holocracy, Sociocracy, Matrix Management, and Lean Management (there are a few of these styles) have been pretty good at documenting the weak areas that causes struggles and failures.

Anyway, I'm quite keen on these approaches; companies employing them are just hard to find.