I believe that private games have their place. If someone wanted to run a playtest of new material in PbP, or run something that could spoil a certain game for others or give unfair advantage (such as Lair Assault, which I'm not sure someone could have permission to do in PbP, but it's still an example)...that would be a good reason to be able to make a game private. I don't personally use the private feature, but if I were to be playtesting new material that has not yet been released, or doing something tournament-style making the whole game private would be a plus.
The same thing could be achieved with privatizing threads...but it's more cumbersome than having a single option to click and guarantee that no one can stumble across it if you forget to make even one thread private.