On the other hand plenty of great books have been written by people in their 20's which is a long way from a full life.
On the other had there is some IMO great poetry written by kids.
But your broader point: "These fields tend to draw upon a whole life's worth of experience -- something that children obviously lack and can't make up for through "winning the genetic lottery"." Yea, I'd agree with that.
Calling a 19-year-old a "child" is really stretching the definition of a "child", in my view. Compare that to chess and music prodigies, for instance, who are already performing at levels above those of most adults even before their teens.[5][6]
[1] - https://www.theverge.com/2017/8/27/16208294/handbook-for-mor...
[2] - http://gary-lindberg.com/do-you-trust-the-nyt-bestseller-lis...
[3] - http://www.hughhowey.com/the-nyt-and-wsj-best-seller-lists-m...
[4] - http://www.politicususa.com/2010/12/02/palin-bestseller-frau...
On your point that he was 19 at the time of publication. Sure you can say he was not a kid when he wrote it, but the act of writing it was not something that just happened over night(and certainly not with a piece of work as long as Eragon). I would still argue that he is a prodigy in the sense that he found success as a writer much earlier than most writers usually do. And perhaps this had little to do with his writing talent. Maybe, maybe not.
This is clearer in some fields than others -- particularly in fields where there are child prodigies, like in chess, music, or mathematics.
In other fields, child prodigies are rare or perhaps even non-existent.
There are, to my knowledge, no child prodigies who've written brilliant novels, or earned the Nobel Prize for Literature (as flawed a measure of talent as it is). There are no children who've composed poems which are considered to be among the greatest in the world.
These fields tend to draw upon a whole life's worth of experience -- something that children obviously lack and can't make up for through "winning the genetic lottery".