I don't think there's a lot of crossover between those verticals: people who want to share photos with friends, people who want to backup photos, people who want to categorise and tag specific photos [beyond what Facebook provides].

And I think each of them is well catered for by Facebook with the exception of organisational features beyond what Facebook offers.

But what you're describing is a photo-optimised interface for Dropbox, not Flickr. Flickr was (and still is) about communities around photographs. And they have failed at that.