Peer to peer doesn’t mean every player has full knowledge. A perfectly valid implementation is to mark one player as the “host”, meaning they run a fully authoritative sim, and the other players get treated as clients, and treat it as they would a server. Only the host needs full knowledge in that case.
In reverse, a dedicated server doesn’t mean the clients have zero or limited knowledge. A naive dedicated server can simply send all the positions of every player every frame to each of the clients.
Another point is that in a dedicated server environmenr the server has a reliable connection, with semi-predictable performance characteristics, whereas if you’re using a PvP model, you’re at the mercy of the the host clients connection, and their machine performance. On a console the performance isn’t as big a deal but on a PC, the host could be mining bitcoin at the same time, or just running on a potato.