Stats are all the same! Concept is key, values can be changed.
So why does Katarina need a rework?
Feast or Famine
Katarina's gameplay is binary, leading to extreme feast or famine gameplay, however I feel that, that simplistic gameplay compared to newer champions such as say Ekko makes her appealing to newer players. When ahead she bursts far too fast, and with Voracity that means that she murders whole teams when ahead. Coupled with the fact she has high mobility only when she is ahead makes her binary. When she's behind she relies on a stat check to be successful and will inevitably lose the fight, with no CC, % health damage or debuffs for other allies to utilize she becomes extremely weak.
I see Katarina as an huge AOE damage, magic damage threat that snowballs upon enemy deaths, but is reliant on others to deal damage for her when she doesn't have her ultimate up, she's like a bomb that requires a fuse to start her up.
Change #1 - No longer decreases the cooldown of her ultimate.
I don't exactly see the point of reducing the ability of her ultimate which is already on a shockingly low cooldown, and with cooldown added to Zhonya's Hourglass and Abyssal Scepter it is already lower, an ultimate should be a high-point of a champion, and it being up every single fight makes it pointlessly snowbally when it shouldn't be.
Change #2 - Lowered duration
With the former change, and the changed cooldowns on Katarina's other abilities in my rework it's less a debuff and more of an adjustment.
Change #3 - Now adds Fluidity.
More on this later on.
Change #1 - The mark now does % health damage.
This is part of the changes to make her less feast or famine. By letting Katarina's mark do magic damage, she can still contribute as % health damage scales as the game goes on.
Change #2 - Sinister Steel, Katarina's old W is now a second cast ability on her Q.
Katarina's old W was binary, had a stupidly low cooldown for no reason and pathetically low AP ratios, yet it still had a use as an non-ultimate mark consumer, so I moved it to Katarina's Q as that was pretty much all I saw it was good for.
This is a new ability I thought of.
Detail #1 - Single target
As much as I like Katarina being an AOE assassin like I said at the start, she should still have some ability to deal some strong single-target damage to squishies to proc her passive, so I decided to make it single target as a result.
Detail #2 - Increasing damage based on missing health WITH a delay
Again, to enable Katarina to assassinate a squishy if she can, basically a low range Zed Death Mark, Katarina deserves some flat magic damage, yet having flat raw damage bursty damage is extremely obnoxious as a result of her passive to squishier champions. So to compensate I've added low base ratios that increase based on missing health with a delay so Katarina can burst at least one squishy, but not all of them at once. Also the delay allows counterplay to Katarina's burst when she's ahead.
Detail #3 - A pretty long cooldown
Again, to prevent Katarina from one-shotting a squishies with a mini death mark multiple times with her passive.
Change #1 - Now does % health damage
Once again to limit the amount of burst Katarina can deal with her passive. This also allows her to contribute if she's behind, somewhat.
Change #2 - Fluidity allows Katarina to blink onto empty space
This change should hopefully make Katarina less binary and allow her to make some cool plays if she manages to score a takedown.
Change #1 - Blade Dancer gives % increase in penetration
This change should hopefully turn Katarina into the huge clean-up crew she should be, if Katarina is allowed to have the entire duration spinning she'll kill some squishies and eventually scale up to killing tanks if left long enough. This means that Katarina's focus should still be squishies like she should be as an assassin, yet still contribute in damage against tanks when she's done killing squishies.
Change #2 - Fluidity extends Death Lotus
More of a whishy last minute idea, but with Katarina's passive no longer lowering the cooldown of her ultimate which has no real use unless you get a 4 man takedown, cleaning up enemies should still reward Katarina's ultimate.
Change #3 - Shunpo can be used with her ultimate if she Fluidity without cancelling it.
In higher level play, Katarina will still remain an extremely niche pick if she can be CC'd, and with Shunpo interrupting her ultimate, coupled with the fact that her AP ratios have to be trashy to prevent her from oneshotting enemies over and over, it leaves her weak. With this change Katarina can have higher level gameplay, Shunpo'ing to dodge CC abilities without being useless afterwards.
That's it, I hope you enjoyed the rework and please feel free to provide constructive criticism.