Some historians may have a greater than average interest in preserving personal documents for posterity. However, historians do not preserve present-day documents for professional purposes unless they are either (1) using modern events to frame an analysis of past events, or (2) historians of very recent history, which is a rare concentration.

Historians avoid collecting present-day materials for future historians for a few key reasons:

First, as you suggested, there is a pre-exising infrastructure for collecting documents. Journalism is very important in this effort, but so are technologies like video and the internet, as well as email, organizational files, print publications, etc.

Second, Historians understand that temporal distance between an era and its analyzer is essential. The various events of the present will interact to have unpredictable consequences. Not only does this mean that it is difficult to determine the causes and consequences of particular events as they are happening, but also that it is hard to tell what events are significant in the first place until years have passed. This is why history textbooks typically stop at least a decade prior to the present.

Finally, historians understand that all historical narratives are subjective, and they don't want to impose their bias on future historians. All historical narratives are formed by the historian's choice, use, and interpretation of sources. Preserving documents for later historians would require making a choice of what is important and what is not -- a personal choice that has no inherent basis in truth.

Rather than attempt to skew future analyses (or simply have a lot of collection work disregarded), historians leave the job of gathering today's documents to peers of the future. The real key players in modern document preservation will instead be journalists and publishers, IT professionals who manage servers and databases, and various types of government record keepers.