There was also an insinuation in that scene that people from the country are stupid, which is part of why Kirk was supposed to be special.
You've mentioned this before, but I think there's quite a difference between
Your aptitude tests are off the charts, so what is it?
You like being the only genius level repeat-offender in the mid-west?
and insinuating that [all] people from the country are stupid. He's asking Kirk why someone with his potential (not to mention family background) is wasting time getting into trouble, and I don't see any reason for reading more into it than that.
Ditto the farm-animals line; yes, it's an insult...
technically, but it's delivered completely without malice. It's more a way for Uhura to admit that she's impressed while at the same time sticking in an amiable gibe which plays on a stereotype neither of them takes seriously, and Kirk replies in the same spirit. It's a little bit of verbal fencing, and nothing more than that.