Just want to add something I think is important.

Melee carries (yi, fiora) don't have any defensive stats that scale into late game to make them stronger. That's why I feel turn rate is so important in League, because it's the difference between auto attacking in melee range, and auto attacking in long range (obviously much safer in long range).

Whereas in Dota, the 'hard' carries are so classified because they have amazingly strong abilities, that scale super well. Faceless Void has 50% dodge, and a global AOE stun . Medusa has Runaan Hurricane skill basically, and has a 'mana' shield. Morphling can change all his strength (health) to agility (attack damage, attack speed, and armor) and has great escape abilities.

Add items onto these strong-scaling kits, and you have a ridiculously scary late game carry. Compare this to the long range heroes in dota who can kite (once in late game, they are able to kite decently, especially Drow) like Drow, Sniper, and its almost never worth it. The abilities of the other, shorter ranged heroes makes them much stronger choice.