Why does brown sugar have to be packed?

Brown sugar holds a lot of moisture due to its molasses content. Depending on the dryness of the sugar just measuring as it could result in a different quantity of sugar each time. Less sugar per cup if more moist or loosely packed, more sugar if dry and more tightly packed. To try to standardize recipes they recommend that it be packed to make a recipe more uniform since we often bake at home by volume. Professional bakers bake by weight for more accuracy,

It's just a means of assuring that you are getting the right amount of sugar. If it didn't specify packed you would be adding about half of the amount of sugar intended. Most recipes call for ingredients by volume. If the recipe called for sugar by weight then there would be no need to pack.

This same answer would apply to recipes that call for sifted flour.

Why do you honestly care? Lol, you might as well ask why paper is white...

because then it'll get hard