You're talking about a government takeover of some sort and it doesn't seem to be happening so far. Governments are skeptical of AI firms.
One would expect that a super-intelligence would have great ideas given the available information, and would even be highly aligned with those leaders so long as the AI it told to keep the leader in power and expand their power.
Of course, some leaders won't want to consult the AI or won't follow the advice. If the AI is really super-intelligent, then we'd expect the politicians and leaders that do follow AI to eventually outcompete those that don't.
This all presumes that the super-intelligent AI is able to optimize for, e.g. political power and longevity, rather than "book smart" or "theoretically optimal".
I’m not sure that’s possible. We often don’t know what the right move would have been, even in hindsight.