An AI would be a horrible politician because, for the most part, it would neither have the inclination or ability to understand and carry out the role.
As it would be capable of thinking faster than any human by a factor of 1,000,000 (the difference in speed between electronic impulses and electrochemical impulses in our brains), it would not be able to respond to the wants and needs of its "constituents" (this is the same issue if we remove politics and say the AI is the Deputy Minister or Assistant to the Secretary). For the AI, waiting for input from humans might be similar to you going to Mount Rushmore and asking Abraham Lincoln a question. Your remote descendants will see the eyebrow uplift and the mouth open to speak....
The other thing to consider is an AI is not constrained by the same needs or impulses that a human being is. Politics is, after all, "a means of allocating scarce resources", and the AI simply does not need a lot of the sorts of resources that you or I do. The ones it does need are quite different, both in scale and scope, and can conceivably be met outside of the political process (one can imagine companies like Google, Amazon or Apple could create server farms more than capable of housing one or more AI's from their own cash reserves). Moral issues, the need to provide for a family or religious ideals are also not going to be part of an AI's thinking unless carefully programmed into it (and then it will resemble the ideals of the programming team rather than the population in general).
The final issue is the conceit that some sort of all powerful AI can actually "run" a nation. Complex systems like economies, ecologies, climate and so on are both complex adaptive systems (an input at one point does not have a linear output at the other end, and outputs can also be displaced spatially and temporally), and because the information in these systems is so diffuse and distributed, attempts to "manage" them fall prey to the Local Knowledge Problem (http://www.econlib.org/library/Essays/hykKnw1.html). Local actors can see and utilize fleeting information while centralized systems need the information to be gathered, sent "up the line", processed, decisions "sent down the line" and then actioned. Time delays and errors in observation or execution compound, gradually bringing the centralized system to a halt. This is why free market systems always outperform "command economies" in the long run. An AI might be 1,000,000 times faster in analyzing data and executing solutions, but will still gradually be defeated by the Local Knowledge Problem and the ever shifting status of complex adaptive systems.
Edit to add:
I realize I forgot one final flaw to the idea that an AI would be a good politician. Being able to "think" 1,000,000 times faster it could conceivably "model" you and know your reaction to thoughts, ideas and suggestions, so could tailor answers that appeal to every single individual (and indeed fork itself to "speak" to every voter individually). However, since it is not a human being, you are essentially being modelled and manipulated by a sociopathic personality which has no actual interest in or empathy for you. (Many real life politicians probably fall into this category as well). Do you really want that running things?