Very interesting. If it worked well enough to depend on you'd soon be dumping hundreds of pages per month. Then to find anything you'd have to stop relying on browsing by date and have to use search. At this point you'd face the barrier of document recognition.

OCR is a generally reliable for text of reasonably good image quality (which is itself problematical for receipts, flyers, memos, and other personal documents). But recognizing genre and attaching meaning to recognized words both remain big challenges. It's an open and interesting question whether current-day OCR would provide enough indexing capability to make the whole thing worthwhile.

Also, I'd worry about the cost/scan-quality tradeoff, angering the user by choosing the wrong compression format (e.g. binarizing when greyscale was needed), and the storage vault.

Your idea may depend on having home file systems more robust than the average person's un-backed-up PC hard drive.

Check out Ricoh's eCabinet, which is an office unit for this purpose.