1. Data retention isn't infinite. If the source disappears from the network, peers will prune it shortly. This is exponentially true in our multimedia-heavy world.
2. Despite 1, if you actually want to delete something you published, you can't. Absolutists will see this as a good thing. Normal people will see this as a problem.
3. Peer-to-peer doesn't work in a mobile-first world, and not enough people will host nodes as a hobby. If all website publishers/hosters have to host a node, then we're just back to the current model but with extra steps.