I don't own any newer console, but I remember people abusing the P2P nature of PS3 Call of Duty MW2 to make ridiculous custom servers that you would randomly connect to. So at least on the Playstation 3, games would connect to arbitrary IPs. Maybe this has changed in the PS4 and PS5, probably for this reason.
I remember playing the Xbox version and you would sometimes get lobbies where everyone had infinite ammo grenade launchers with no reload, or other similar funny stuff. I really enjoyed myself when I was lucky to end up in one of the matches.
Pedantically, maybe. But the host of the match lobby was randomly selected and it could have been any of the peers who end up as the host. When the host leaves, one of the remaining peers becomes the new host. So, all peers have the capability of being client and/or server.
You connect directly to one of the players in the lobby, also known as a peer. It isn't a dedicated game server, just the game itself. I think it qualifies very well as P2P.
