Most games use P2P because it's a hell of a lot cheaper to run 1 or 2 servers for matchmaking and offload all of the simulation and network cost to the players,

Most games use P2P because it's a hell of a lot cheaper to run 1 or 2 servers for matchmaking and offload all of the simulation and network cost to the players, rather than hundreds or thousands of dedicated servers, and because their developers were focused on consoles where cheating is much more difficult. If you're already using dedicated servers for whatever reason, though, the computational cost of strictness with player input is not so great in the grand scheme of things.