His thesis (at least for the final chapter) is that we like bureaucracy because we like the idea of living in a society where the contours are pre-determined, and thus, highly predictable -- more like a game than authentic play. In a society that was more like play than a game, our lives would be more unpredictable, but, at least according to Graeber, we would be truly free to express ourselves authentically.
I also like the metaphor of societal design as Newtonian or Darwinian. Newtonian society (our current world) is a society where things do not emerge, things do not change substantially, and where, if you know the current state, you will be able to predict its future state almost exactly. In contrast, a Darwinian society would be a society where things can spontaneously emerge (mutate), where things can change radically, almost unexpectedly in relation to different contexts, and where, if you know its current state, you have no guarantee that you will be able to predict its future state.
In my opinion, if we are ever to get to a distributed organization for humanity, it would be a society that would be more Darwinian (organism-like) than Newtonian (machine-like). In this sense we could move from a society where we are not "cogs" in a proverbial "wheel" - where we all attempt to fulfill a specific function and spend our whole lives doing the same job - and instead move towards a society where we are spontaneously exploring a possibility space with unbounded potentiality.
Here we come back to Graeber and his ultimate conclusion, which is that we cling to our bureaucracy (instead of getting rid of bureaucracy with something like a basic income) because we fear this possibility space, and we fear this unbounded potentiality. Or, using his theme, we fear play and true freedom.