Historians love diaries, and encourage people to make them and archivists to collect them. Why is there not also a push for archivists to sift through modern rubbish pits too?
I'm guessing there might be a desire to (what better way to get a thumb on how people are actually leading their lives right now), but there's a mix of privacy issues, sheer volume and cost.
Archaeological examination of refuse is important because it can tell us mundane facts about a society; what was eaten, what materials were commonly used and for what purposes. Certain types of materials being found discarded can show that a society had contact with certain other societies (for example one could find a discarded vessel made in a certain way or of a certain material not native to the region in which it was found).
The utility of compiling knowledge about our own current societies by observing our refuse is a solution in search of a question - generally speaking, we can readily find any of the answers one might ask about our current societies that could be answered meaningfully by going through our trash, by virtue of being live witnesses to the daily goings on of our respective societies.