First, it wasn’t a potentially fatal scenario. It was a simulation.
Ya, i's kind of hard to experience fear in the face of certain death when computerized klingon ships go 'boom!' and all you get is a red light that goes beep. Really effective.
As Jeyl points out, there is no “fear in the face of certain death” when the cadets know it’s a simulation. There isn’t even a fear of failing the mission when the cadets know that nothing they do can affect that outcome of the mission.
So how about this as another way the film might have handled it:
The instructors want to see how the cadets deal with failure, so they create this test for them to fail. They do not acknowledge that it is literally impossible to win. There are rumors that nobody has ever beaten the test. The administrators refuse to confirm or deny the rumors.
Cadets who take the test hope to be the first to beat it, and know that if they fail they have to handle the failure with composure.
Kirk, after trying and failing twice, discovers that the simulator is programmed to ensure the mission’s failure no matter what the cadets do. He concludes that “the test itself is a cheat,” so he decides to cheat and respond to the resulting accusations with a “You’re all a bunch of hypocrites” defense. In the process, he also exposes the true nature of the test, which had widely been suspected but never known for certain.