The major problem - one of the major problems, for there are several - one of the many major problems with governing people is that of who you get to do it; or rather of who manages to get people to let them do it to them.
To summarize: it is a well-known fact, that those people who most want to rule people are, ipso facto, those least suited to do it. To summarize the summary: anyone who is capable of getting themselves made President should on no account be allowed to do the job. To summarize the summary of the summary: people are a problem.
-- Douglas Adams, The Restaurant at the End of the Universe, ch. 28.
As those who've read the book know, the government of the Universe has solved the problem by making their President a figurehead, and letting all the major decisions be made by someone who doesn't believe the Universe exists.