This is a just-so story without any empirical evidence.

The model of hierarchy is too simplistic. If you zoom in on the nodes you will see a more complex structure. It's not just one person but a host of people, operating in a semi-formal somewhat also anarchic structure. At every level of the hierarchy there is ample backup that will keep the system from collapsing.

Then there is also the dimension of efficiency that is completely missing from the discussion. Hierarchical systems might be more fragile but also much more efficient.