Because being organised makes you more effective. With your 'throw it all in a box' system, you have a high barrier to finding documents in the future and this discourages you from doing so. However, with a more organised approach you are more likely to retrieve specific documents.
One example: Some mid-priced electronic device breaks a few months after you buy it. You might weigh digging through all the paperwork versus shrugging your shoulders and throwing it away. I would go straight to the warranty document and also look at my credit card issuer's warranty/returns policies(if any), and I would return the item for a replacement or refund. No biggie, only a few minutes work and I as a consumer prevail in exercising my rights.
Sounds boring but I believe it is definitely worth making the effort.