The majority of web apps do at least one thing extra: they try to correlate user data to provide something more out of it (be it Google for improving search, be it facebook for providing social related suggestions, aka. ads)
This seems cannot be done at least in the current stage of Unhosted. I don't see how this can be done with encrypted storage that the provider can't do a lot even with polymorphic encryptions.
you would need decentralized search algorithms. i haven't looked at that much myself, but there are some projects out there that seem interesting. to give an idea: when my friend is logged in, his browser could run algorithms that send me recommendations. think about how you receive information on twitter: not through centralized algorithms, it works through peer-to-peer retweeting. at least as a research topic, it is very interesting :) but you are right, there is stuff that's hard to do. i think the most challenging one would be google search.
This seems cannot be done at least in the current stage of Unhosted. I don't see how this can be done with encrypted storage that the provider can't do a lot even with polymorphic encryptions.