If it were kg/m^3 then it would just be proportional to density. The idea of BMI is that there is a healthy range of weights for people. Fatty tissue has a slightly different density than lean muscle, but not that different, so BMI wouldn’t be very sensitive if it were just the density.
So, knock off a length factor and you have something that correlates well with fitness. You can think of it like, you get one factor for height, but your girth, you only get one factor even though it’s 2d.
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