Afaik melee carries can work in DotA for the simple fact that HP and AD are 1 combined stat (strenght) on some heroes, thus the simple act of building strenght item make you tanky and damage heavy at the same time turning most strenght heroes into Nasus lategame.
And i can guess that the simple existence of Black King Bar factors a lot in the viability of such carries, in LoL Mercurial Scimitar is but a far cry of the previous.