It would be really cool, but the reality is that websites that uses similar kind of data are usually direct competitors and work as closed gardens (Facebook vs Google+, Vimeo vs Youtube, Bing vs Google). But I do hope that at least multimedia tags will be able be dragged and accepted by other websites (drag a video tag to YouTube, drag a pdf to dropbox, etc)
Hmm, I see it as the opposite. Why wouldn't Facebook want to register themselves as a sharing output for images and text? They want us to share as much as possible, and this would just make it easier for users.
Otherwise, you'd see sharing menus across the web with "Google+, Twitter, etc." on them and no Facebook. Not a position I think they would want to be in.
