I find it interesting that you singled out Katarina as a character who can't take down an entire team by herself. I've done so plenty of times against competent opponents.
Not taking away from any of the other mages, but if yo uknow how to play a character right, you can get a pentakill with most of them. --- Its me, said Jace. Watching me play Scrabble is enough to make most women swoon. Imagine if I actually put in some effort.
well without resets, Kat's damage is way lower than that of the high damage casters, EVEN if she gets to fully channel her ult (lol) and gets to always be in range to use W every time it's off cooldown --- "Somebody get me up so I can die fighting!"