It would be useful for pulling back pages that have fallen off the internet and are not in the wayback machine.

Thats a use case I have hit a few times. I even started backing up useful posts just in case they died.

http://gigablast.com/rants.html is an example. Its a really good insight into the creation of a search engine which really should be preserved.

One that did dissapear but has since come back is this post http://widgetsandshit.com/teddziuba/2010/10/taco-bell-progra... which I went looking for a few years ago but had dissapeared from all search indexes.