n(n-1)2 is a strawman itself: a 1000-person organization will probably have 3 levels (900,90,9) with each person communicating mainly with team members or the level above or below, so O(nlogn) communications channels, probably.
The problem is that each set of middle managers cannot represent the bandwidth required to express the problem to their subordinates or the solution to their superiors.
At the top, you have a board of 10 people. Each one of these is making decisions and receiving orders for 100 people. This sort of structure is going to have some serious communication latency and a loss of data as it traverses the company heirachy.
