It is though? You probably wouldn't be aware that hormonal disorders can exist and affect height, so you'd massively underestimate how tall people can actually get.
Now I want to know how those people fit in a distribution. It could still be a continuous function.
Of course it's continuous, but (guessing) it's closer to power-law than normal - the tails are fatter than you'd think, and when you try to estimate variance from a sample you get an underestimate.