It's not that different from a service I used to use a loooong time ago, called Paytrust (which got bought by Intuit). I changed all my billing addresses to an address they gave me. (Actually I think Paytrust might have updated the billing address on my behalf for most of the accounts.) Everything they received, they scanned in. The benefit was that they also marked it down with who the bill was from, how much it was, etc. then you could pay them all with just a few clicks. Also, they would do the same thing which was talk to the billers and convert it to an electronic system so that they didn't need to handle paper bills. You could also look at the scanned image of the document if you wanted to, and you could also order a CD at the end of the year with all your documents as well.

So this sounds like Paytrust minus the bill-paying, but with a stronger emphasis on getting rid of and letting you easily view all your mail. (Edit after looking at their site some more: They also will send you the original item if you want it... something that doesn't really apply as much to bills. Although Paytrust did sometimes forward things to me, like a new membership card or something.)