...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).
Although the writes are expensive and very infrequent reads, the cost of having a failed read can be so expensive (like, your house, rapport with the IRS, etc).
Shoeboxes are horrible. They're not fire-safe, not waterproof, difficult to secure, difficult to distinguish, easy to spill and easy to crush. Get a safe and dump things in there.