Let's take Orianna as an example.
Assuming there's a wave i want to clear off, i use Q. At the same time Zed decides to go for me since i'm closer. He shadows in and is most likely done murdering me before i can bring my ball back with E to chain R and W. Not saying it happens every time, of course, but it only needs to happen once. At that point you either need to run out of lane or are dead. Zed at lvl 6 has simply too much single target burst, and has a bonus damage amplification (if i remember right) which have no reason to be there.
Some champions can obviously handle Zed than others, but it's generally a pain to deal with.
I would recommend spreading his ult's damage over 1-2 seconds longer to let people time to react.
Otherwise it'd also help if Zed had a split second of downtime after shadow so people can have the time to register what the heck just happened.
Or, you know, give him a mana pool to play with, and decent/high mana costs so he can actually pay for the insane damage he outputs.
Replaced everything with zed to emphasize how little you actually involved kat specific traits (the only one being grievous wounds).
Everything you said was either a huge exaggeration:
"She shunpoes and is most likely done murdering me before i can bring my ball back with E to chain R and W."
Something that is a common trait of all assassins:
"At that point you either need to run out of lane or are dead"
Or inability on your part to have reasonable reactions and instead of getting better you want the game to baby you:
"I would recommend spreading her ult's damage over 1-2 seconds longer to let people time to react.
Otherwise it'd also help if Katarina had a split second of downtime after shunpo so people can have the time to register what the heck just happened."
Do you know how much fucking time a second is? Pentakills happen in a second. The only thing katarina has going for her is speed because her damage is gated by reset potential and manalessness. You shouldn't be reacting to katarina, you should be taking preemptive action and thought against when she tries to go in, like with all assassins. You can't react to a talon flash E ulting either, you have to be aware that you're in a position that allows him to do that and should have more vision/less shitty positioning.
That's why a lot of newer players think assassins are strong while the best players think assassins are generally on the weaker end of mid laners. Assassins only work if they get kills. Assassins only get kills when the enemy doesn't respect their damage and makes mistakes. Mistakes happen a lot for new player but barely at all for high skill level players. This creates a dynamic where assassins are actually weak in the meta at a high level, but they're getting calls for nerfs by the majority of players because the majority of players aren't good.