trophy child
n. A child used to impress other people and enhance the status of the parent or parents.
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Research finds that by grade three, one cannot tell the difference between children who came to first grade knowing their ABCs, number facts, or even how to read and those who came as academic "blank slates."

The notion that exercises of this sort produce a smarter child or a child who consistently achieves at higher levels is bogus.

The fact is, these so-called "jump start" programs are a huge waste of money and time. They appeal to parents who are desperate for what I call "trophy children" — children they can show off, brag about, and (it should go without saying) live through.
—John Rosemond, “'Jump start' programs a waste of time and money,” The Charlotte Observer, October 30, 2002
The pitfalls of spoiling children are well known, but many parents
don't realize that in subtle ways they also may transfer their own
ambitions onto their children, burdening them with too much pressure too soon, Hausner says…

"You've got particularly what I call the trophy-child syndrome.

The child has to fit into the perfect picture of what the family is
supposed to look like. It's an expectation . . . and some very high achievement standards are set," she says.
—Dawn Bonker, “Children of paradise,” The Orange County Register, November 18, 1999
1990 (earliest)
In my contacts with older couples now raising their children from a new relationship, I am impressed with the intensity of their parenthood, especially their eagerness to be the perfect mother and father, and to have the near-perfect child — a "trophy child." The parents want to do everything right "this time," so they dote over their trophy children.
—Lewis P. Lipsitt, “Trophy children,” The Brown University Child Behavior and Development Letter, May 01, 1990
This sense of the phrase trophy child is part of a long series of phrases that use the adjective trophy to mean "something used to impress others and enhance one's status." The series includes trophy house (1981), trophy wife (1989), trophy girlfriend (1990), trophy tree (1991), trophy car (1992), and trophy job (1995). I'm still looking for trophy trophy.