I HAVE HAD THE GREATEST IDEA!!!
Katarina is probably one of the most complained about champions in the game at the moment. I have an idea that might make Katarina more of an assassin than just wrecking teamfights. Here it is: Make her ult a single target damage over time spell THAT DOES NOT NEED TO BE CHANNELED that goes relatively fast and has around the same cooldown as her old ult. This would make things like zhonyas and qss viable because you could completely negate her ult damage, but she could still assassinate people. This would make her more of a single target assassin rather than teamfight assassin, which is what people hate. Of course the damage needs to be adjusted so that it's not as much damage as her old ult because that would be op. I think this might solve the problem, but if you hate please don't rage.
The ability could show her throw a knife that makes them bleed and almost looks like Bloodseeker's ult from Dota 2.
Thank you :D