Why has no-one started building such a service (or, at least not in a public way) on existing cloud services (eg AWS or Rackspace) and/or create their own global network?
Data backup and replication is not “difficult” – and neither is the concept of distributed (and replicated) storage (LeftHand Networks was doing RAID-over-LAN a while before HP bought them).
So – why is this not available as a service to which you can subscribe (or use anonymously)? Incorporating in a ‘friendly’ country, offering anonymized connections (fully encrypted, etc), and giving a client that works a la Dropbox or Box.com.
There should be lots of companies who would love to offer a service like this – it should be fairly lucrative, and pretty easy to setup.