Intermingling with other people's data is fully possible. For instance, I may store a list of friends, with URLs for their unhosted storage and public keys to check their signatures, and I would compose my news feed by connecting to each friend's unhosted storage node. The web2.0 aspect is perfectly possible. What is hard is search. Instead of centralized search, you could implement some form of social search in apps. Or make all users together carry a DHT.
The goal is bringing free software to the web. Free software seems to be stuck in installed software (be it installed on your PC or installed on a server), and that's a shame, because a lot of software that people use nowadays is hosted. Everything we have achieved is becoming almost meaningless if you use a free kernel and free libraries and free drivers and a free browser, to access a non-free facebook, or a non-free google, to find content on a non-free youtube, or a non-free google docs.