I don't know, I'd think that a site is fairly unlikely. After all, that opens you up to charges of ~art theft~, which we all know makes you about 72% worse than Hitler. Hasn't stopped people in the past, though.
I think the most likely route is regular users wanting to make some kind of backup. Furry artists do love to randomly decide they suck and delete fucking everything on a yearly-or-so basis, so people scraping their own favorites would make sense. Also, the helpdesk 'web professional' segment of Furry probably has more than a few people who would cobble together something slightly more complex than Pi's FAbomb above in order to brag to the peer group that they've got a copy of ALL THE PORN. Or, as you said, if said people are concerned about FA randomly vaporizing at some point.
Actually, if it is regular users, you'd think there'd be example code floating around. Anyone seen any?
While we're on the subject of the FA eschaton, my money's on 'lack of time/fuck-given after Sciggles gets around to oopsing Piche'.