User blog comment:StrategicMagic/Carry by Proxy - Why (Some) Assasins Don't Fall Off Late/@comment-132.241.109.39-20121206221359

You're partially correct in your explanation for "falling off late game." However, there's a second reason that I feel you missed.

LeBlanc, Talon, Veigar, and other single-target damage dealers can very easily kill any squishy they want to. This makes them a terror in lane, but when late-game rolls around and teamfights start happening, you need to be worth more than your counterpart. Single-target burst nukers and assassins kill one person and then wait for cooldowns. While their cooldowns are up, they're very vulnerable and are almost always killed immediately after their burst. If an assassin who got fed off his lane kills the enemy AP carry and then dies himself, he isn't making any headway in the teamfight; it's now a 4v4 with your team's potentially most fed person dead. Even if you survive, you're still useless while you wait for cooldowns and the enemy team fights an even teamfight. That's in the best case scenario. There's always the possibility that you go in on an assassination that the enemy is ready for and they kill you before you can burst them.

Assassins have insane damage throughout the game. The reason they fall off late is because they don't have the opportunity to put that damage down. Split-damage AoE carries like Karthus, Morgana, Orianna, and Lux can burst down multiple members of the enemy team, if not all of them. This is why they are picked in high-elo and competitive games.

There are a few assassins that can burst an entire team, though, namely Katarina, Diana, and Akali. The key here is that they all have really short cooldowns and/or cooldown resets. They burst one person out, then another, and another, all in quick succession. Under the right circumstances, those three have the ability to put out the most damage of any champions in the game, and they excel in late-game teamfights, whereas Talon and LeBlanc are at their weakest in large fights.