First, it keeps the story going. Had it been a single torrent, there would have been a lot of stories, and then on to the next thing. That this may also be more commercially successful does not escape me.
Second, it give the government a chance to really put their foot in their mouths. With Wikileaks, the US mostly said nothing about the details. With the Snowden documents, government officials respond to one thing, then further documents reveal where they are lying or weaseling.
Third, once the torrent is done, the government can do a whitewash investigation, and then say "all that is behind us. We've fixed the problems and now we're focusing on the future." It's not possible to have a whitewash investigation unless you know all that needs to be covered.
Fourth, this is a complex issue, and the process of reporting lets the reporters have time to get feedback from the analysis of other people, and integrate new information into their reporting.
Of these, I think #3 is the most important advantage to a stream over a torrent.