Kirk and Saavik are the only officers (in canon) whom we've seen take this supposedly no-win test.
Now we don't know if it still exists in the 24th Century (I assumed the Klingons would be replaced with some other hostile, territorial race).
I also tended to suspect this was a test for cadets focusing on command. Doesn't seem like there be much use in making med students, counselors, and science officer, most of whom probably aren't likely to command a starship under normal circumstances. Those in engineering or security, I suppose could go either way.
My question is how do you think Picard, Riker, Sisko, Janeway, etc. would handle this test?