I had similar idea a while ago, although it didn't involve bitcoins and I never actually acted on it.
How do you solve the problem of an evil storage node provider who detects that you're trying to recover a file from backup, blocks it and sends you a "transfer X BTC to my account to get your data back" email?
Files are stored in multiple places and Storage Nodes will be asked to send files on a regular basis, for example, to ensure there is sufficient redundancy for a given file or if the end user wants to sync the files to a new computer.
The storage nodes also have no knowledge of who owns the file or what the contents are. Combined with the fact that they'd immediately stop getting paid for the other files they're hosting, it seems like the ROI for one of those evil nodes is pretty negative.
How do you solve the problem of an evil storage node provider who detects that you're trying to recover a file from backup, blocks it and sends you a "transfer X BTC to my account to get your data back" email?