When I watched the movie I laughed and thought it all ridiculous. I've since been shown that having well-intentioned, self-aware, cooperative people in government is probably more important than their intelligence.
Also, Joe seemed genuinely interested in helping everyone, and didn't seem to neglect the needs of significant portions of the population to achieve some ideological goal or another.
Maybe there's such a thing as being too smart to have power.
That being said, it is a society who elected the smartest guy in the world president, and then when a smarter guy came along elected him as the successor.
IMO that is a depiction of some kind of meritocratic utopia - exactly the opposite of what we have, on all accounts mentioned above.
Now honestly it is just a goofy movie premise, and we should not look too far into it, but sometimes it is fun to go full nerd.
Although to be fair,some of that happened before Idiocracy came out.
With the public money used for sports stadiums, that element of the movie to have government sports teams is slowly coming true also.
Further, colleges receive public money but are not free to attend for most students. And I am not talking about "free" from the students perspective, I mean most would not be permitted to enroll if significant tuition dollars were not deposited (unlike public schools, for instance). Also, plenty of colleges are private but have NCAA teams.
I agree that it does wrongly depict poverty as a major indicator of intelligence.