So it isn't JUST because their presence is essential. Something else is here. Because, as you say, it is not possible to convince you that the GM's sway could ever, for any reason, be eclipsed by another participant being essential. Even if that other person were in fact more essential, it's irrelevant, because being GM is all that matters, period, end of discussion.
So, what is it? It isn't "no GM, no campaign", because you've just said that "no X, no campaign" isn't enough. We've established just before this that it's not "player consensus supports them", because no matter what the players think, the GM always prevails. Nor is it labor, neither in personal expense nor time invested, since that can vary in absolutely enormous ways and can easily be less than that of any single player (e.g. the GM doesn't own the books, one of the players does, or the GM uses another player's account for something etc.)
So the GM isn't privileged by having the support of their players, nor by being an essential requirement for play to proceed, nor by always being the one who does it depends the most. What is the difference?