Interesting, I really like this idea. Useful work instead of performing wasted computations is definitely going in the right direction.
What are some use-cases for this? For example, if I owned a company, I would still want internal data storage within my company, if anything, to save costs on bandwidth. The only applications I can think of (right now) for this kind of distributed storage is similar to what I would upload to dropbox, which is free up to a certain point. And, I suppose, for those concerned about censorship.
Pandaisftw