Decentralized websites should be treated the same way than static HTML websites. Everything what you publish there is public. If someone forks your site without your authorization, essentially it's a copyright violation, but other harm would not be done. (A CC-BY-NC-ND Creative Commons license would be an interesting option to prevent this, at least legally. It would only allow non-commercial forks, and forking without commercial intentions is kind of pointless. Even better would be a custom "no fork" license which only allows redistribution of the original, not a fork.)
So what would be the use cases? Mainly, blogs and other informational sites, and open-source/open content projects. One of the prime examples, which is often mentioned of decentralized web advocats, are "uncensorable" blogs for opposition activists in authoritarian countries.
Sites which sell something can also be built with this technology, but they cannot include customer data. Communication must be established via other means, an example could be tools like Retroshare.