I think this depends on lifestyle. I know that if there's vital information on a piece of paper I need to photograph it (or type it up) and email it to myself because the paper will be lost/destroyed before too long. I could invest in a fireproof safe but it'd be another thing to move and take up space which I don't have a huge amount of. Something emailed to multiple email providers and copies stored in Dropbox, etc is unlikely to lost.

And when you're dealing with a high quantity of information, good luck searching through thousands of sheets of paper for something.