I've arrived at a somewhat similar conclusion, tentatively, through a slightly different angle, but yes I agree wholeheartedly; your response to the game, your response to the reveal, is meant to make you experience what it feels like to be be Big Boss.
It operates on numerous levels, as MSG games are wont to do, but that is the crux of it. Everyone was craving to play as Big Boss, to be him, to experience the awesomeness of being the greatest solder of the 20th century with no holds barred. And that's what we got complete with Big Boss's sweet leather jacket and a replica of "his" arm available to anyone who wants it.
But we forgot that being Big Boss is hell. It's not just about commanding an army of killers and dominating the battlefield. There's the army of mooks idlozing his legend without having ever really met him, the Spartan life of fanatic military living with nothing even close to resembling normal life - just a fascist military operation focused purely on war and on his cult of personality. He has this constant ache of something missing in his life, and we feel that in a nested way through his proxy.
We were conditioned to crave revenge - the levels of hyped "THIS IS IT", "I'M GOING NUCLEAR" were at fever pitch before the game launched. And, technically, we did get revenge. But it felt hollow and meaningless when we learned the truth. At the narrative level the game uses Venoms arc to create that hole in us to comment on the nature of revenge - that there is no satisfaction. It never goes away. Other characters talk about this.
Mechanically it also does this with Quiet - an overpowered invisible sniper who utterly has our back in the field. With her disappearance we are suddenly left with a gap in our tactical arsenal are are forced to functionally compensate by relearning how to tackle encounters that we previously had no trouble with. A part of the way you interact with the world is taken from you, and you feel its loss. For me, the fact that there even is a way to pause this from happening is an incredibly generous concession. Kojima could have made his point far more strongly.
Through this proxy of Venom we then, as you say, are left with the game in front of us. Personally, due to the nature of the reveal of the cut content (released in official footage right after launch), I feel this is a part of it the statement. We are left with a game, called the Phantom Pain, and the unshakeable feeling that something is missing. Many players began to rage against Konami and the corporate politics that must have led to this.
This brings us to Big Boss, a man with a hole in his life that was caused by the whims of international politics. A man who has had something taken away from him that he felt (rightfully) entitled to, and now lives with the inescapable emptiness. People also forget the first half of Kojimas final message. Yes, we are Big Boss (our emotional reaction is his) but he also says we are Big Boss too. Kojima and You. Creating story and meaning through art, and especially interactive art, is a symbiotic relationship. Kojima can write and program and deliver the story of Big Boss, but it's not complete until it is played and reacted to. At the end, he says from now on it's up to us. All that remains is your reaction, to complete the legend of Big Boss and learn what brought him to 1995.
Some people are screaming and yelling, some are writing petitions, some are punching mirrors - but Big Boss reacted by starting a revolution against the systems that led to his pain. MGSV is the going to be one of the last in a rarer and rarer breed of big budget game in todays corporate gaming landscape. What are you going to do about it?
Also; don't forget about how Kojima did the same thing in MGS4 as well. Just as MGS2 gets written off as post-modern drivel, the ideas that come closest to the surface in MGS4 get written off as fan-service. MSGV kind of does the fanservice thing in reverse compared to its partner in the Solid Snake games. Only instead of the hollow grab-bag of elements of the previous games being recombined and mutated into a monstrous representation of what an iterated world with no human factor feels like, MGSV delivers the real fan service deal and gives you the true Big Boss experience - only to find that his life is hell.... even though on paper we knew that all along.