I don't think that the movie was proposing that the issue or solution is eugenics based. I would argue that educated people are probably able provide a better education, and that uneducated parents are less likely to be able to provide their children with a quality education.
I don't specifically remember Idiocracy really going into depth about "passing good genes".
50% of the produce we consume is grown in the California central valley. The rest is grown in a few areas of the Great plains and in Florida.
Most of the food you see growing anywhere else isn't for people, it's for livestock.
I think you are overestimating just how much food "the land" can provide. You need around an acre a person for subsistence farming, and that is assuming you live in a region that has a decent climate, that you have irrigation, and have access to modern fertilizer and pesticides.
As far as hunting and fishing goes..... If a large sector of the population had to live off the land, the wildlife likely wouldn't last a single season. The only reason we still have the wild animal populations we currently have is because there are strict regulations monitoring the amount of people who hunt and fish.
Early Americans were able to devastate a larger healthier ecology with a tiny fraction of our current population. Most of our country's natural Forrest and woodland were already destroyed and artificially rehabilitated over a hundred years ago. We have very few old growth Forrest for us to actually live off of.
If it weren't for petrochemical fertilizer the natural nitrogen cycle wouldn't be enough to sustain our current population. Since the invention of the haber process in the 1930s we are all just a bad year away from food insecurity.