In order to carry an entire team, a champion has to win lane and snow ball first.
Most champions that scales really well off of stats from one or two kills are often also very easily shut down.
For the purpose of winning a game solely (or at least mostly) by yourself, I would recommend: Riven, Vayne, Gnar, Fiora, Akali, Rek'sai, and Fizz for top.
The key aspect of these champions is that they have great synergy with one particular item in game that will give them a massive power spike. As well, most of them have an ult that practically guarantees a kill if they use it.
It makes it easy for them to snag a kill in lane, hit their spike before their opponent, and proceed to carry the game. As well, these champions are extremely mobile, so enemies can't run away from them and deny them further kills.