AI?! AI?!
Like, haven't you watched all the robot movies? Do you need to rewatch the Terminator Series, and I mean all of it?

Okay, more seriously now, AI could never be the solution to human leadership, unless of course, somehow the machines were programmed with actual human emotions. And that's already making them human. But that's what we need, notwithstanding the troubles it brings.
I'm pretty sure you've considered how human beings keep making the same mistakes generation after generation? That's our emotions acting out, and the same mistakes occur because the emotions never change. Now think from the other direction and consider all the good that persists in the world. Same explanation.
Emotions are important. Messy, yes, but important. And suggesting an AI Government is suggesting one without emotions. Believe me, that's going to be one cold, cold era.

Still, it makes a great prompt for a story! :D