Many times people have tried to come up with rewarded p2p file storage and/or seeding ideas.
SO far the only thing that has worked is a central company that rewards people for making space available, and even then it does it by only rewarding them with space, not with any kind of "money".
If they tried to reward people with any kind of "money" they would probably not be able to operate because the number of cheaters they get who want to cheat them for some extra filespace is trivial compared to the number of cheaters they would get if they tried to reward them with anything that could be cashed in, including cryptocoins since those could be cashed in at an exchange.
So tons of people have spent shitloads of hours trying to solve this and that corporate approach is the only actually working solution so far.
All the distributed storage open source apps and freenet and so on and so on have all looked at the problem, so unless you have a genius solution forget it; if you do have a genius solution go explain it to the people in #tahoe-lafs channel on Freenode.
-MarkM-
My response to that is that only files that are being downloaded get rewarded. I.e., if you have a junk 1gb file that's full of meaningless data, normal users aren't going to download it. Since bandwidth in a torrent would only be used when someone is downloading that's one way to get rid of cheaters.
Alternatively, we could remove the file aspect and just make a proof of storage: swell the block chain size so that only big hard drives could hold it, and have two clients: a web client that works like any web wallet, which you can mine normally and deposit to, and a downloadable qt that does the same and serves those requests to uphold the block chain like servers. They would be paid dividends.
Or alternatively alternatively, you could rent out your hard drive for space and there could be a companion sign up site like media fire. Each account would be limited to a certain amount of hard drive space and people renting out their computers for space would be paid when files are accessed. As bandwidth for particular files increases, there could be requests to copy the popular file to new clients to increase accessibility. Files would be encrypted on upload and would be copied to additional computers if nodes went down. If more people install the client and rent out space, the amount of storage on the site increases. The only problem is that the website is a point of failure - by necessity it'd have to be centralized or hosted by people running the client. And there's still the problem of how to adequately find out when you deserve a reward...
It's tough.but it should be a problem worth solving?