I'm having trouble finding a source at the moment, but I believe that the BBC attempted this a few years ago. They eventually abandoned the project because as the editors needed the full resolution file of everything they were using to ensure the shot was in focus etc., storing them locally was a better option. I can't really see that changing in the future either.

An NLE that checked out files from a remote server and then made edits to a text based file from which anything could be shared would be very useful though.