I can see your point, but it sounds like you believe in character as of something inborn, not acquired. To give no second chances means to filter people selecting for a proper character. From the other hand second chances might nurture a character.
> Once you start taking shortcuts, you tend to keep taking them until it results in a colossal screw-up.
So maybe for educational purposes academy needs to provoke cadets to take shortcuts and to make them into a colossal screw-ups?
Educational environment is not a "real life". Their goal was to pass exam on calculus. They did everything they were able to do, including the cheating. It is the cheating in educational environment, in real life it would not be the cheating, it would be a healthy cooperation. Or maybe not so healthy, because they screwed it up, by sharing not right answers, but mistakes. It is hard to judge, because there is such thing as a psychological narrative, there is a psychological context for all this. Each cheated cadet had his own context, his own story that came to a cheating.
In a high school I was ready to share my homework with my friends, and sometimes I got unacceptable marks because a teacher was able to see cheating and marked all with low grades. I got low marks not because I cheated, because I helped others to cheat. Was I demonstrating a lack of character, or a high morale character, who was ready to take additional risks to help his friends? It depends on my own narrative. From the one hand, it might be a lack of character, due to inability to say "no" to my friends. From the other hand, my friends might be more important for me than my grades. (Really I don't know what it was, because I know that I have troubles with saying "no", and at the same time I never bothered with grades, I knew that I would manage something acceptable, especially in math, I was good at it).
This anecdote here is an attempt to demonstrate that it is hard sometimes to judge character by assessing behavior only. It is even more hard on artificial educational environment where rules could arbitrarily diverge from real life.