Carries are great initiators. Just not melee related ones. Ezreal does it great by attacking, and teleporting away. If a team fight starts and someone on their team is not at 50% hp, im not doing my job. Ashe has a stun, which is one of the best initiators in this game. A good team knows how to harass a carry in a team fight. The tank will go straight for you, someone will reserve a stun or 2 for you. At least in my level of play that's so. I main ezreal, or have started to do and i carry my team. I can take 2-3 people by myself due to being ranged. I have never been this succesful with any melee champion, because they do not have the huge advantage of being ranged.
Theres ELO for a reason. If it wasent implemented, you would be playing against people that would wreck you, day in and day out. This also allows for people to learn which champions work in their categories and play them. Theres a reason yi, eve, and the rest are champions you que dodge in high ELO. They do not work, thats why they have been remade by the devs.
Also, all my points are directed at a 5vs5 scenario with a competent team on both sides. In my experience playing since beta, any champion that is meant to deal damage is preferred to have 2 of the following 3 things: A way to get in and out. A way to deal damage without much danger to themselves. A very nice CC. Ranged carries fit most of these categories, melee ones do not.