Several aspects of the universe were developed over time and several writers will have been involved. The insane scarcity of spots for the academy is something from early TNG that pretty much falls by the wayside later on and goes unremarked. Like Chief O’Brian starts off as a nameless con/nav officer with lieutenant pips and then somehow becomes a non-com with a rich war history, a wife that hates him, and a child lost in time temporarily.

They needed to keep the Wheaton out lukewarm in case the child actor wanted out or had to go for another reason. So they dangled his acceptance to the academy in front of us so it wouldn’t be a surprise when they finally got rid of the boy (the boy?). It’s a bit far fetched that super warp genius tapped to become a traveler of space and time would not get in as many times as he didn’t, for various questionable reasons.