[tlrobinson]

"it's unclear what the motivation for running an instance of this kind of P2P application would be"

Incentivising P2P applications is one of the interesting problems Bitcoin could solve.

People have talked about building P2P storage applications using Bitcoin, which is essentially what this would be, except if you stop paying into the network the files should be transmitted to some 3rd party of your choosing instead of being destroyed.

Perhaps some splitting scheme such as Shamir's Secret Sharing could be layered on top.