Not to make a nitpick in your point because it's a good one, but it made me wonder:
How different would the height measure be if it were standardized like IQ? E.g., how likely would someone who is in the 90% percentile in 6th grade be in the 90% percentile as an adult? From that perspective, I imagine the standardized height "re-test" correlation is a lot less than 1.0 (although it would certainly be close to that with two measures of height as an adult).
0.8 correlation with adult height for boys aged 4, according to [0]. The real study [1] is paywalled but looks legit. I'm guessing it's even higher at age 12, though it might be confounded by puberty soon after.
How different would the height measure be if it were standardized like IQ? E.g., how likely would someone who is in the 90% percentile in 6th grade be in the 90% percentile as an adult? From that perspective, I imagine the standardized height "re-test" correlation is a lot less than 1.0 (although it would certainly be close to that with two measures of height as an adult).