as a Katarina main, I feel like I've got a decent understanding of what actually makes her op. I know people are complaining about her ult, passive damage and her E resets, but I feel that these are her intented strengths. I think that her true balance problems resides in the lack of clarity on when you're in range of her passive dagger and also that she might have more damage than needed on her Q. Her base or AD scaling might also be a bit high for her all-in potential considering the fact that she has an AA reset and pretty good AD ratios on her spells. I do also think that her passive dagger might be staying for longer than needed. Sometimes I feel like it stays forever.
IMO she is too strong right now. Part of it is because of the meta and the rest comes from numbers. One thing that I also hate about Katarina right now is the fact that tank or semi-tank Katarina is just flat out better than ap Kat. Full ap Kat is pretty balanced if not really far ahead. Tankat on the other hand is really really strong even when being a bit behind. A tank should not be able to kill a squishy as easily as an assassin.
some possible nerf areas
1) This one is the most important one in my eyes and one that needs to be done: give an indicator for both players on the passive dagger's range. Where you are and aren't safe.
2) Nerf her q base damage. (maybe like 25 at lvl 5?)
3) Nerf her q cooldown. (1 or 2 seconds would probably do the trick)
4) Nerf the time the dagger stays on the ground. (maybe by half a second or a second)
5) Nerf some base AD, scaling or how tanky she is.