You're missing the point of the role completely.
Except proper mages and some fighters/assassins can carry, and that is their role. In the world championships, for example, sometimes a mage, Orianna, would annihilate the enemy team even if their own team was not necessarily leading. This fits the metaphor of picking up your team and carrying them on your back. There are also cases where there may be a ranged AD champion who is doing extremely well, however, the rest of their team is also dealing loads of damage and doing well. In this case the ranged AD champion is not "carrying" their team.
My point is, that unlike other roles, carry is no something you chose to do in champion select. You don't pick a champion and say, "Oh, I am going to carry." Whereas with the other roles, when you pick a champion you also pick the role. When I pick Leblanc I can decide to be an assassin or a mage or both. When I pick Mundo I can be a tank. When I pick Caitlin, I pick to be a high damage dealing champion, being a carry is situational.
tl;dr;
Carry is situational.
The only reason ranged AD damage dealing champions are referred to as AD carries is because it is a much shorter name and that in the meta they are the ones who are supposed to carry. But you should all know that people are not forced to play the meta, and that just because something has become a common term does not mean it is always 100% correct.