...but when you do need that obscure piece of paper you need it right now.

Think of a filing cabinet(1) as an exception or error handler. In a perfect world, you could just burn your receipts and statements after you've finished with them. In our imperfect world, it saves you a world of hurt when you can snatch that stuff at a moment's notice.

(1)(Do sell the filing cabinet though: Bankers boxes are much easier to move about or squirrel away in the closet).