Sorry a little bit off topic but your post made me think of it..
If society glides into a genuine direct democracy I think traditional bureaucratic institutions, like the departments you refer to, and societies relationship with them, could change considerably.
At the moment they are pretty large, static, and hierarchical, I think that is largely because of a traditional social pact, or deal they have with government, and basically with society, which is along the lines of they will keep everything functioning, not strike etc, as long as they get a level of employment certainty and benefits often not seen in private enterprise. They don't have to be as efficient or as results driven, and in return might not see as high salaries but have stability.
The government doesn't want to rock the boat with this bureaucracy as any failure in their services gets translated as failure of the government, but under DD that sort of status quo would lessen, the public may demand more, or perhaps find creative ways to achieve better results. I could see a sort of Flux completely disrupting these traditional departments, perhaps fluid and shared population controlled ways of managing social level systems, or open results based private competition.
The reason I mention this is because down the track, you might not have the departments you mention, and a different method of achieving the results you want would need to be found.