Given the rules, rewards, and penalties, along with the fact that they isolated Kiyo so that he couldn't participate in the exam; it would serve to develop the dynamics and characters of each class along the plot of the Second Grade, functioning as the regular .5 volume acting as a setup, but since this isn't the case, there might be something more.
Due to the apparent lack of risk of expulsion and the absence of variation in the fluctuation of class points within the same grade, there is no need for cooperation and along with the exhaustion caused by spending a week on the uninhabited island, it would result in that only the diligent students would participate taking it seriously.
Therefore, at the end of the first day, in order to motivate the students, the school will reveal/add a rule penalizing the defeated side: that among the students who have lost twice, one or all of them will be expelled.
Now that the whole plot of the Third Year seems to revolve around Hiyori; she will be one of those eliminated or only just her, triggering a conflict within both sides as they fight and sabotage amongts themselves with some wanting to save her and others wanting her expelled, concluding with Nanase and/or Ichika becoming the martyr:
-Nanase's motives: She wants to provoke a change in Kiyo's ways that could be triggered by Hiyori's presence; she tried to get both Shiraishi and Ichika on her side so her expulsion might shift their stance; Housen might behave more wildly and recklessly without someone by his side; just like Arisu, she could exert influence from the outside should the plot required it.
-Ichika’s Motives: She doesn't have/know the purpose of her life nor does she have a stance regarding the feud between Nanase and Ishigami; is aware that Hiyori could/would be targeted; she meet Kiyo previously this one is thrown in quarantine triggering the trope of the unacknowledged last encounter; the treadmill girl who might also be the one who beat those two first grader could potentially be a wroomer becoming her replace/upgrade.