Even given the smartest, most perfect computer in the world, it can give people the perfect, most persuasive answers and people can still say no and pull the plug just because they feel like it.

The same is not even different among humans, the power to influence organizations and society entirely relies on the willingness of people to go along with it.

Not only this sci-fi dream is skipping several steps, steps where humans in power direct and gauge AI output as far as it serves their interests rather than some objective ultimate optimal state of society. Should the AI provide all the reasons that they should be in charge, an executive or a politician can simply say "No, I am the one in charge" and that will be it. Because to most of them preserving and increasing their own power is the whole point, even if at expense of maximum efficiency, sustainability or any other concerns.

But before you go fullblown Skynet machine revolution, you should realize that AIs that are limited and directed by greedy humans can already cause untold damage to regular people, simply by optimizing them out of industries. For this, they don't even need to be self-aware agents. They can do that as mildly competent number crunchers, completely oblivious of reality out of spreadsheets and reports.

And all this is assuming an ideal AI. Truly, AI can consume and process more data than any human. Including wrong data. Including biased data. Including completely baseless theories. Who's to say we might not get to a point AI decides to fire people because of the horoscope or something equally stupid?