My boys are a bit older. They play Minecraft on a PS4. They create a world and then just play together. I don’t think it is offline but Friends Only. So the game stays private. I think this is a great way of enjoying Minecraft. Like yours they talk constantly about what they have built, what they are going to do next etc. I limit their playtime to 1 hour max per day. They can choose what to play. Other great games on PS4 are Lego World, Lego Star Wars, Rachet and Clank and Little Big Planet. All are local coop except Rachet which they play by taking turns.
Oh no. The trisolarians are coming!