Seems that the kingdom is just trying to raise a loyal and powerful pawn for nefarious purposes.
Not neccessarily nefarious, but it's in a Kingdom's best interest to provide the best education possible to gifted individuals within their sphere of influence.
The thing here is that the
school just cares about the accolade, and isn't particularly interested in what the child actually wants or needs.
Which is a thing you see all too often when it comes to Prestigious Schools.
If the difference in development and interests was so great that Olivia couldn't Fit In socially they'd have had a point in suggesting she gets whisked off to this School for the Gifted.
But as-is, she doesn't stand out too much, despite her obvious potential, and actually fits in socially. Which... well.. doesn't really happen that often in Real Life™...
So ripping that away from her, defeating the whole point of her being In School And Making Friends would be.... monumentally stupid.