@Oeconomist
It's pretty obvious that the hatred between Shakuyakus and Botans is a superficial one brought on by the way the school's set up. That the students would warm up to those they're paired up with in the ball by getting to know them over the course of practicing for the ball instead of just staying in a state of judging them based on them being Shakuyaku or Botan is something that the author should reasonably expect someone to be able to infer, I think, since the latter mindset has been shown many times throughout the story to be the main reason the Shakuyaku vs Botan mentality persists. While you dismiss my examples as not really showing why the Shakuyakus and Botans grow closer together, both sets of interactions (the blue haired lass and her partner to an extent but in particular the Misa and Kagura interactions) show firsthand that the method of the Shakuyakus and Botans being forced to get to know each other better works.
In addition, at a couple points throughout this arc Yukino says that the ball is working because it brings the Shakuyakus and Botans together working on a common goal. You could argue that if they were just forced to interact with each other through classes or something that it would cause a fair amount of conflict, but I think that the 'common goal' aspect of the situation is a good insight as to why the Shakuyakus and Botans grow closer throughout the ball as well.
Also worth mentioning is that at around chapter 30, Shakuyaku and Botan students come together in a much smaller extent to find a key that some Botan students lose, and that event plays out similarly to how the ball does (with the Shakuyaku and Botan students involved warming up to each other). Though this incident, due to lasting for such a short amount of time, doesn't really have much of a long-term effect (except arguably that it caused Kumoi to be willing to get along with Ookami from the start, sparking their subplot), I don't think it would be that much of a stretch to say that this event sets up/foreshadows the solution to the Shakuyaku and Botan conflict the ball arc employs.
And while I think I make it sound like the ball is 100% effective in resolving the Shakuyaku and Botan conflict throughout this comment, I do think that there will be more to come with the Shakuyaku and Botan conflict. I mean, the ball between Shakuyakus and Botans is a first-year event only. There's no way the author could handwave away the prejudices of the entirety of the school based on a ball that only occurs between the first-years. If the ball arc does end up being used to ditch the Shakuyaku and Botan conflict, then I would agree with you that it does a poor job of explaining how that could happen. But based on where we are in the story, it's pretty absurd to argue that the events of the ball arc show the author's pushing the conflict aside.