(maybe provably impossible)

If it is provably impossible, I would feel much better with a proof; this seems like a reasonable goal for SingIst, to look at proofs of computational complexity and upper limits on computer power, and get an upper limit on the optimization power of an AI (perhaps a few estimates conditional on some problems being in different categories or new best algorithms being found); then to come up with some reasonable way of measuring lower and upper bounds on the optimization power of various organizations (at least a generous upper bound on all existing organizations and a lower bound on some big ones like the US government).

I would be EXTREMELY surprised to find that a lower bound on organizations was higher than the upper bound on AI, but if so it would be good to know already, and if not the research would probably be worth doing anyway and a good showcase of the actual extent of the problem.