That's why you need digital signatures and authorship tracking. Copyright just by itself would already put an end to every P2P alternative or at least stop it from ever gaining any mass traction. On the other side if everybody put a digital signature under their published work, others could mirror it without themselves becoming responsible and you could have take downs of objectionable material via blacklists.
So far very few of the P2P alternatives implement anything like that and even those that do just have arbitrary accounts that don't link back to any real person.
This of course goes against the whole anonymity and privacy focus that has been predominant in this field for the last 20 years. But if we actually want a real alternative to the Web, not just some toy app with a dozen users, I think it's the only way to go. And of course you could also have a layer of indirection in there to provide some anonymity or pseudonymity, so it's not like those things would be impossible, just reduced.