Katarina's kit doesn't work. Here's why.
The current Katarina is designed to be an assassin who has high mobility and damage. She uses her daggers to deal heavy damage dodge skill shots because if she gets hit by too many, she's toast, and so she can get into and out of anything (unless she gets caught) but if she takes down her target when there's more kills to be had, she's godlike, but one piece of her kit stays from this description, makes it difficult for her to be effective against at least 60% of champions. The piece that doesn't belong in her kit is her ultimate.
Her ult, Death Lotus, locks her in place until it does the damage it needs to in order to get that kill. It completely stops her much needed mobility and turns her into a target. In order for it to be effective, two conditions must be met: she needs to be close to her target, or in their path of movement (not likely, since it's better to avoid walking through her if possible), and she needs to avoid any hard cc.
There are two major issues with this. The first is in order to use this effectively against multiple opponents (which really the only thing that makes her passive useful) she needs to get close and stay close. Doing so severely decreases her life span and is guaranteed to provoke cc, drastically reducing her ult potential. Being a target means she must either avoid damage (she can't move while ulting) or deal damage swiftly after the kill. Her rework made this extremely difficult, as she must wait for her daggers to land before spinning with sinister steel. The vulnerability of Death Lotus was justified before her rework, her old q e w combo was swift and impossible to dodge, and she could easily overpower people after getting the first kill in a teamfight, but not anymore. What's more, over 70% of champions have abilities that can quickly stop her ult (I am including ults), therefore, since the only way to miss is to forget to aim, she is effectively countered by 70% of champions. I say countered because if kat could easily get kills without her ult and without being fed then she would be overpowered. The second major problem with her ult is that it does not synergize with the rest of her kit in any meaningful way. Let's look at it piece by piece. Her passive: her ult does good damage over time so that should get her kills right? And if its on cooldown her passive should get it back for her, ya? As i mentioned before, her ult refreshing cooldowns doesn't help if doing so nearly gets her killed, and in order for kat to kill without her ult, either she needs to be fed, or her target needs to be weak and/or injured and/or alone. This kind of situation is hard to come buy when the other team knows you'll try to take advantage of it. Sure, you could finish the job another teammate started, but if Katarina needs to rely on others to get her kills, then she's a failure as an assassin. Her q: the way her q and her ult work together to fulfill her role as an assassin is that they both deal damage. Her w: the extra speed might be useful for getting into position, but really Kat's w sets a dagger and helps her move. She can't move while ulting, the dagger is nice, but like with her q, it only helps by dealing damage. Her e: shunpo does help Katarina get into a good position to ult, but depending on who it's being used against, there is no good position to ult. Even if used against targets without hard cc, she still has to do enough damage to get a kill. Mid to late game, tanks and juggernaughts are tanky enough to withstand her ult even when not interrupted, therefore even tanks counter her. The fact her ult applies grevious wounds isn't even that useful. If needs grevous wound, morellonimocon no longer builds mana, so getting it's not a waste for her.
Some ways her ult might be changed:
Her ult (or another ability) could apply cc (all other assassins have some form of cc)
She could be able to run with ult active
She could be able to shunpo with her ult active (and nerf ult to balance)
Her ult could throw daggers at people (that either land behind or on them, activating sinister steel) (and nerf sinister steel to balance)
Her ult could be replaced by another ult, where she throws 2/3/5 daggers in a target direction
Riot could make her a new ultimate. Recent champions that riot has been made have been as creative as they've been fun as far as they've been balanced. I bet if Riot made another, different, ultimate designed specifically for Katarina, they would do an excellent job of it.
In short, Katarina's ult does not synergize well with her kit, and so it should either be adjusted or altogether redone.
Please read this Riot