What's Wrong With Katarina, and How To Fix It
Katarina, as a champion, undoubtedly fulfills her design goals. Weak early, strong late, countered by CC, etc. Katarina's weaknesses are her atrociously weak early-game that leads to her being bullied easily, and the fact that endgame, Katarina's combo can be stopped in its tracks by crowd control (CC). However, these weaknesses, while meaningful competitively (Diamond+), are actually fake weaknesses that are completely overridden in lower tiers.
Particularly, I wanted to focus on her second weakness: Crowd Control. While it's true that a single stun makes Katarina completely useless for the whole teamfight, I've found that, when I get fed, I can burst someone before they can even react to the stun. A successful Katarina should be forced to at least go through 1 second of her Death Lotus, however, often, a basic ability combo plus one or two daggers of Death Lotus are enough to instantly kill an enemy. By the time I am stunned, the teamfight is already over. I was able to kill a Warwick before he was able to use his Infinite Duress (R), due to the massive front-loaded burst that eliminates Katarina's weaknesses. Katarina somehow needs to be forced to use a decent, counterable length of her Death Lotus to kill enemies (at least enough reaction time to use Flash).
Basically, in non-ritobalanceteam language, Katarina's Death Lotus kills enemies before they have a chance to react, removing good and healthy counterplay, because she can kill teams before a single CC goes off in the endgame.
I believe that Death Lotus should still be able to decimate enemy teams; however, the damage needs to ramp up over time; each dagger deals more damage than the previous dagger. For example, the first second of Death Lotus deals a quarter of the damage, while the next second deals around three-quarters of the total damage. This could be done one of two ways: either an actual damage increase (Death Lotus daggers deal xxx damage, increased by xxx damage for each subsequent dagger), or reducing the damage per dagger of Death Lotus and adding "% of missing health" damage to it. While this second strategy seems more elegant, I fear that this might not be meaningful, as Katarina's Q-E-W combo would chunk enemies down enough to make this new weakness null. The first suggestion seems more meaningful.
While these is a significant nerf to Katarina's early-game, I believe that compensatory increases to base damages, particularly on Sinister Steel (W), can maintain Katarina's early-game at its current level, while making sure that her meaningful weaknesses remain important in the end-game.
Note that I don't want a flat-out nerf to Katarina. In fact, Katarina is one of my favorite champions. I enjoy the high-paced gameplay, and the strategic thinking (when and where do I ult so I can get off maximum damage without being instantly CCed); however, in the endgame, these weaknesses become all but irrelevant and she just turns into a "wait in the brush, press E, press R, pentakill" champion. While Katarina should have immense strength for getting through the difficult early-game, if she becomes fed, she becomes oppressive instantly, with no possible counterplay except for extremely skilled players.