There’s nothing shoddy about the BMI. However, it’s intended as a measure to track & compare populations. (For example, it tells us pretty convincingly that America, as a whole, has gotten much, much fatter over the past century.) The BMI doesn’t make sense as a way to judge individuals, for all the reasons you mention, but it definitely isn’t Adolphe Quetelet’s fault.

By the way, Adolphe Quetelet, who “wasn’t even a doctor,” was a statistician — which is exactly the sort of person you would expect to invent a statistical tool for measuring the characteristics of a population.