I have never seen a champion this broken

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She's not broken since her kit hardly even revolves around the reset passive. The most she can do with it now in games vs evenly skilled players is use it to escape or setup more damage for her team.

Even pre-rework it was exaggerated since teams needed to make a myriad of mistakes to actually fulfill the conditions for a Kat player to clean up.

She's tuned down low because Riot hates AP assassins, it's really as simple as that.

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However, I do agree with the rest of the champs you have mentioned since they are indeed fundamentally broken.

Any reset mechanic is fundamentally broken because it bypasses the cooldown of an ability, something that is supposed to inhibit a champions power in a certain window of opportunity. This is what forces design choices that make these windows tiny and narrow to the point of almost impossible to pull off.

Tristana has been a staple of competitive play for years due to her reset mechanic allowing her to quickly and easily clean up fights.

Eve had a resetting move speed buff that accomplished something similar.

Khazix is regularly abused for the reset and clean up potential.

Katarina is focused on resets as her core identity and that's a fundamental design flaw which will typically always result in a broken champion. A broken thing does not need to be overpowered, it can be broken and because of that be underpowered and kept deliberately so. As with all fundamentally broken champions, its the nature of the kit that causes the schism.

Should probably have mentioned Kalista in that last grouping too because of her gate being mobility and yet her passive ungating her mobility allowing her to move and attack simultaneously. Some aspects of some champions just never had any business being implemented in game (troll pole any one?).