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.)
At the time it was IIRC, $15/mo. Now it's like $10. Personally, I feel outbox's $5 is a sweet spot - it's well south of $100/yr, and is about what I pay for locally filtered bottled water per month.
Also changing the mailing address has significant impacts for things like proving residence (for schools, etc), so that is a pain that Outbox users might avoid.
Honestly, I'm surprised we haven't seen more a modern mobile/tablet version of Paytrust come around.
"If applicable, and unless you direct Outbox otherwise, Outbox may also, now or in the future, direct the third parties who send you mail and/or bills to send certain items of such mail and/or bills electronically to an email address provided to such third parties by Outbox specifically for that purpose and for that purpose only, in which case you authorize Outbox to do so in its sole discretion for as long as your account for the Service remains open."