Why does Kat get to feed and still be a huge threat?
She isn't, once again this is where I said that's an over-exageration.
Katarina is a very binary champion, she either doesn't do much, or she can do enough damage to take out 3 people.
This isn't as reliant on how fed she is or her itemization as it is on her ability to get resets.
If the enemy team zones her well and prevents her from jumping on their carries to get that first reset, the fight essentially becomes a 4v5. As long as low health targets have enough sense to stay back and leave when kat approaches, kat's potential can be reduced to her basic QEWR combo. The issue is many people disregard her and end up getting caught out of position and give her a reset, unlocking her damage potential.
This design means kat can always do decently even when behind if the enemy team plays poorly.
However, it also means that kat can always do poorly, even when ahead if the enemy team plays well.
This is how it is balanced. You might see that as toxic, but it's the exact opposite in my mind. If the enemy team does poorly, they are punished, if they do well, they are rewarded. This holds true to a decent degree regardless of kat being fed, or kat being shutdown.
The other point I would bring up is katarina specifically spikes in the mid game. Her early game is abysmal and her late game is about average for an assassin. When she comes out of lane 0-3 and everyone is then fighting for dragon thinking "wow kat got shutdown, easy game" she's still probably strong than a conventional mid laner or ad carry. This isn't op, this is knowing your power spike. Ad carries have late game, mages have early game and late game. Assassins have mid game. That time where not too many resistances have been built, tanks aren't really full tanks yet, there aren't any GAs, zhonyas, banshees, or QSS built yet.
This is the time that assassins thrive, especially kat because of her reset potential. This is when you should be weary of katarina. "but she lost laning phase" she's supposed to, kat is bad in laning phase, yet she's still considered a good pick because of how great her mid game is. All you have to do is not get overconfident and keep in mind the fact that you haven't seen katarina at her strongest yet. You think a leblanc with only those items wouldn't blow up a lucian with those items? What about an akali, or a zed? Assassins thrive off of poor play, it doesn't matter if they were shutdown, if you're stupid enough to get caught or challenge things that you shouldn't during their powerspike, you will be punished for it, the same way an assassin will be punished late game by trying to dive the enemy carries if your team plays well and peels to some extent.