I feel the opposite - kids are being treated like machines, with their performance judged at every step. Treating a kid's brain like a "performance muscle" is gross to me. There's a vast emotional world being papered over to squeeze out performance from children.
Student athletes learn more about their bodies and performance than students do about their brains.
"why do you think the lessons aren’t crossing over into academics?"
I don't think this. My anatomy and physiology class covered the basics about different processes. Things like sleep, stress, and attention were things that were covered in some assemblies or ad-hoc (at least from an applied standpoint and not necessarily deep technical standpoint).
I agree its really important to learn how one's physical body and habits shape their felt experience and to truly realize you have a lever to change it.