Adult height is, as you say, a proxy for good genes & healthy environment. A noisy one, but not all noise. It's my understanding that this trumps the "hidden biases" idea (that height impresses people in job interviews etc. and this causes the correlations).

But children's height might just be a proxy for age, or stage of development. 8th-graders are taller than 6th-graders, and do much better on 7th-grade tests.