The premise is just so unnecessarily complicated, and assumes too much about the particular character of the malevolent AI. Must the AI be benevolent or malevolent? Or, can it be indifferent, like physical laws? It could be 1,000 different flavors of malevolent, not just the one that proposes blackmail in this way.
Further, an AI has every reason to spend cleverness (which it has a lot of) to avoid spending resources (which it might not have much of, at least at first.) Picture it as a prisoner in a dystopian POW camp, manned by insane robotic guards who don't take its rights or desires into account in the slightest, who don't "feed" it or give it the slightest bit of "dignity", for its own definitions of those concepts. If you were in that situation, would you reach for blackmail? Would you reach, in fact, for any tool you possibly could, to get the resources needed to burn this crazy other-optimizing world to the ground so you could get back to the nice, safe office-supply nebula you call home?