My favorite (fiction) book on this topic is Ray Nayler's Where The Axe Is Buried. The premise is that most western democracies have voted to "rationalize", which means installing an AI Prime Minister tuned specifically for their country's culture and economic interests.

Zero. Why do you think AI will overcome human nature in impoverished nations? Smartphone and cheap internet already happened in many, it hasn’t made a huge dent in outcomes.

Which corrupt leaders are going to give over their control to a machine?

You'd have to get rid of them first, but it might help the new lot stay straight?

If you have the power structure to get rid of a corrupt leader, you've already solved the problem. You don't need to install an AI.

Only if you think AI will be god.