From Star Trek 2: Wrath of Khan:
SPOCK: The Kobayashi Maru scenario frequently wreaks havoc with students and equipment.
KIRK: Self-expression doesn't seem to be one of your problems. ...You're bothered by your performance on the Kobayashi Maru.
SAAVIK: I failed to resolve the situation.
KIRK: There is no correct resolution. It's a test of character.
From Star Trek (2009):
SPOCK: Furthermore, you have failed to divine the purpose of the test.
SPOCK: The purpose is to experience fear. Fear in the face of certain death. To accept that fear, and maintain control of oneself and one's crew. This is a quality expected in every Starfleet captain.
We know Star Fleet academy does some messed up things, like testing Wesley's ability to make life or death decisions in an emergency.
Wes enters room 101 where the psych test will take place. It is empty except for a chair. At first nothing happens, then he hears a noise outside. He goes out, and the corridor is deserted. He hears shouting coming from the environmental lab. He goes in and sees a technician trapped under a pipe. Another technician is frozen with panic and won't leave. He frees the trapped man, and drags him out, but has only just enough time to get him out before the lab is sealed off. He sees Lt. Chang standing over him. He tells Wes that this was the psych test, confronting his fear of having to choose between saving one man and leaving another. This was because the same situation resulted in the death of his father. Wes had overcome his fear and made a similar choice; whom he chose was not as important as the fact he actually chose; Wes had passed the test.
That unexpected test seems a lot better than the Kobayashi Maru.
It seems every cadet already knows the Kobayashi Maru is an unbeatable scenario. How is it an effective training tool when it is common knowledge you will fail. It isn't a real life and death situation. How are they going to experience fear, in a simulated game, which they already know the outcome for?