Re: Moving the goals?
"Yes, that's why it is height^2."
As mentioned by other posters, humans are 3-dimensional, so using square is not correct. As also mentioned above by other posters, humans are more 'cylindrical' than 'spherical' so maybe using the cube of the height isn't very correct either.
"BMI is a decent measure of a population's tubbiness, which is what it was intended as."
Except that actually, it isn't, because it takes into account only mass, without distinction of whether that mass is fat or muscle. This is made worse because muscle is denser than fat.
Given the 2 issues above and given that fat tends to accumulate round the waist while muscle gain is more evenly distributed, a better measure of 'fatness' would be
mass/(height*waist circumference)