The facts that Troi took the test, passed it (eventually) and then was promoted may not be as directly related as they look. At best we can say they're correlated.
Agreed. This test seems to play a fairly minimal role in the lives of two TNG heroes: essentially, it helps them out of boredom. We don't hear of other hero or sidekick careers being significantly influenced by tests of this nature, even though everybody is taking special training left and right, both within Starfleet and in the civilian environment: Ro took extra tactical studies, McCoy was a specialist in space psychology, Picard knows a bit about everything.
There are various milestones in Starfleet careers, but very few appear mandatory. Spock eventually got command without taking the no-win scenario test; various others who had no original command ambitions, such as Sisko, ended up in a commanding position. There are probably plenty of ways to sidestep the Bridge Officer Test, too, and plenty of ways to become a blueshirt Commander or Admiral without ever even visiting the bridge of a starship.
Commodore Stocker made it to flag rank without having commanded a starship, for instance.
In TOS terminology, we might argue that Stocker had commanded plenty of Starfleet spacecraft, and the particular merit he lacked was the command of a Starship...