I could hypothetically imagine a world where an AI could run a country, but we are a long way from that point with the existing systems that we call "AIs". They are optimized to produce responses that look human-like, but their model of the world is different from a human's, and pretty limited.

But even aside from that, the point of voting is to keep the interests of the leader more-or-less in line with that of the public. You're probably going to need some kind of mechanism like that. Specifically with AI, understanding how to align future increasingly-capable goal-directed AIs and human interests is a major issue; it may not even be a problem that can be solved.

https://en.wikipedia.org/wiki/Friendly_artificial_intelligence