Early video games never had much of a story. Metal Gear was among the first to add story to its gameplay. The player controls Snake, and together we've told this story over the years. As the series went on, the player jumped between multiple characters like Solid Snake and Naked Snake, and the story evolved into the legend that is the Metal Gear saga. In this final Metal Gear, it was only right to return the role of Snake, the main character, to the player. It's saying that from now on, you make the story. It's saying this is what it means to come full circle and complete a story. If this were a one-way medium like a movie, V's ending wouldn't have been possible, but this was a game. This made it possible. Taking a story we've told together over the years, and placing it in the hands of the player. That was the real intention behind V.
If the player wasn't a doppelganger to Big Boss in V, that would have meant Big Boss himself dying later on. And long before V, back in the original Metal Gear, the player (acting as Solid Snake) had in fact killed Big Boss. That made it important for this final instalment that the player once again enters into the story and brings things full circle in their own way. I think it's only at that point that the story truly belongs to the player. This is "creating the story together with the player," something that can't be done in traditional media like movies and books. This can only be done in a video game. That's what makes V the culmination of everything we've always done since the original Metal Gear.