It absolutely goes full circle, it just doesn't do it in the way you expect.
Lets roll through everything this games deals with.
Big Boss turning evil. He does exactly this in MGSV. Just because he's not eating babies doesn't mean he's not a despicable person. He turns evil because he turns his back on everything he once stood for. Big Boss chooses to fight the Patriots by acting like one, he uses information control to turn Punished Snake into an attack dog. We see Big Boss become the man that we see in MG2, a child soldier raising piece of shit. Meanwhile, the good doctor carries on Big Boss's legacy(which depends on your moral status, but I'm gonna guess it's canonically good)
Setting up the Patriots A.Is. Pretty simple, the history of the Patriot AIs is finally revealed.
Eli and David. Eli was in Great Britain, fled to Africa for some Lord of the Flies shit. David, however, was too smart for his own good. It was at Foxhound that he met Master Miller, who in turn turned Snake into the greatest warrior who ever lived.
It is explained how Otacon really is the greatest engineer of his day. Where Huey has trouble getting Salenthropus to move, Otacon uses its remains to create the most advanced Metal Gear known to man.
V. Ocelot is running the show, he's a Rival living a Lie. Ocelot is this story's O'Brien, through words that control the subconscious, he shapes you, the player, into Snake.
Lastly, just because you aren't playing Naked Snake doesn't mean you aren't playing Big Boss. Big Boss is not a man, Big Boss is a title, a legend. It is embodied by many people, carried on throughout the generations by people like Solid Snake. You are Big Boss, but you are also you, the player. The idea here is that Big Boss was never Jack, Big Boss was the person behind the controller.