In summary: Instead of trying to decide if a piece of paper is important enough to warrant keeping, just toss it in a box. By the time the box fills up time has decided that question for the bottom half of the stack.
When you have a job that touches a boatload of miscellaneous crap, sometimes knowing what drawer to look through -- if and very occasionally when -- is all you need. (The time saved from filing the miscellany more than made up for the occasional search. Further, those searches sometimes triggered unanticipated and productive thought processes, in the process of skimming other materials.)