Iirc Wesley’s disqualification was age related. He was a boy genius but there is enough of those in the post scarcity utopia that Starfleet isn’t dumb enough to recruit all of them as officer, their lack of maturity could get them or others killed.

It was practically reverse affirmative action in that brightest youngsters could compete for a few slots to get into the academy a few years earlier. So he was not going up against the Miles O’Briens of Starfleet. He was going up against the Julian Bashirs who can ace nearly any standard test with their eyes closed.

Last thing Starfleet needed was impulsive teenagers to find them selves in command of veteran crewmen, react horribly to be given advice contrary to their current orders and get people or themselves killed. The Academy is for future officers, not the enlisted equivalent ranks that O’Brien filled. Wesley would have made a great crewman, he’d have made a terrible officer.