When talking about edge cases I could come up with ones that don't involve the cloud. And in those cases maybe I don't need to replicate a server, but instead I just need to represent a very small amount of data in an encrypted form that can be operated on homomorphically.
While I don't have a fleshed out idea on how to apply it, the one area that I'm interested in thinking about homomorphic encryption being applied is POS financial transactions. My gut (and this is just a gut, not backed by in depth thought by any means) is that homomorphic encryption as a building a block could allow you to design a secure and significantly better replacement for the existing credit card (or even chip and pin) system.