Even if "only" 10% of elite kids go on to become elite adults, 10% is orders of magnitude larger than the base percentage of adults who are elite athletes, musicians, etc. This doesn't sound "uncorrelated" to me so much as "not as strongly correlated as one might expect."
And describing something that happens 10% of the time as "rare" sounds a bit weird, like referring to left-handedness (also about 1 in 10) as rare.
A child prodigy in tennis may find that their body didn't grow in such a way to be a pro as an adult. If your opponents are taller, stronger, have better VO2Max, etc. than you as an adult, it doesn't matter how good you were as a child--they're going to beat you as an adult.
Chess, of course, now provides the stark reverse contrast. If you weren't a child prodigy in chess, you simply will not excel against the competition as an adult.
One can enhance cognitive functions by strength training: https://pmc.ncbi.nlm.nih.gov/articles/PMC8534220/
Aside from time travel, the best way to improve in very important things is through strength training.