BMI does take height into account.
It’s basically the straight-forward old height-weight tables turned into an equation to give it a scientific gloss - ooh, math - and eliminate male-female differences from consideration.
Explaining how to calculate BMI takes up as much space on the page as the old tables, and either annoys or intimidates most people.
With the tables you can just look and see, okay, if I lost 7 pounds, I’d be in the normal range, whereas with BMI, you have to plug the numbers back into the equation and re-calculate.
Anyway, even if everyone were a healthy weight, there will always be 15 in 100 over the 85th percentile,etc. More math. Does anyone in that school know what a normal distribution is?
The BMI tables are total and utter nonsense. They barely make sense for Chinese people. By the BMI index, Tom Brady is overweight (6'4, 225), and LeBron James (6'8 250) is 12 pounds from obese.