More Words, Deeper Hole

The core idea behind BMI is that "height cubed" isn't the right relationship. A 6' tall man is going to be significantly less than 72% heavier than a 5' tall man of the same build because humans don't get wider as fast as they do taller.

The problem with BMI is that "height squared" is too slow, which is what leads to it only working for a limited height range. In reality, the factor should be somewhere between 2 and 3 but do you want to try and tell random people to use an equation with a non-integer power?