Zed most definitely isn't a good guy. His goal isn't to improve the Kinkou, if it was he wouldn't start an order of his own, instead Zed's goal is to make Ionia a powerful nation that fully uses the amount of power within it. It's the same as Irelia, but what separates the two of them is their methods. While Irelia wants to make a capable army where the strong defend the weak, Zed wants to make Ionia that values power above all else. Zed will kill anyone who gets in his way, even his father figure or his long time friends, he uses shadow magic which actively disrupts both Ionia's harmony and the spirit realm as whole (see Nocturne lore) and intends on militarizing the natural magic in Ionia, leaving many magic based locations uninhabitable by magical creatures like the Vastaya, forcing them out of their homes. I mean, his short bio literally starts with the words "Utterly ruthless and without mercy", so no Zed is in no way a good guy.
I think you got Kat and Talon mixed up. Kat is a lot like her father and firmly believes in Noxus and everything she does is for Noxus, while Talon, with the little to no lore he has, is the one who pledged his loyalties to Kat's father, and is currently investigating his disappearance. But I'd agree that I wouldn't call either of them bad guys, they're about as much bad guys as Garen or anyone else who kills to serve their country.
Kha'zix, Eve and Noc (and this also applies to Tahm and the other voidborn) are all kind of in the same batch. None of them really kill because it's "fun" or because they want to, they do it because they HAVE to. Kha'zix and the voidborn are beings made of anti reality, anytime they get mentioned they're described as off putting and "wrong". They're basically sentient objects given one purpose: Help their creators destroy the world. Kha'zix in particular seems to devour anything that would further his evolution, and in other stories the Void mostly feeds on magic and/or organic material. Kha'zix isn't really evil because you can't categorize him in a human like morality scale because he's not human, he's like a robot with only one function that he HAS to follow.
Eve, Noc and the other demons aren't evil at all IMO. They're spirits who unwillingly were brought into this world through negative emotions, and the only thing sustaining them and preventing them from going back into oblivion is feeding on the same negative emotions which spawned them in the first place. They either torment mortals or disappear forever, not much of a choice in the matter. They're about as evil as any IRL predators, are lions evil because they hunt and kill other animals?
Qiyana is someone that I'd say is actually pretty bad, if not evil. She's way more than "just a brat", she's so self centered and so deep in her inferiority complex that she pretty much lacks empathy for anyone else, including her own family. She's completely willing to kill, hurt and manipulate others in order to further her own selfish agenda, which let me remind you if she DOES end up being empress, she'll want to go to war with the rest of the world. Pretty evil if ya ask me. Also consider the fact that IRL anyone who would cripple their sibling or manipulate them emotionally by causing them serious trauma would be considered evil, so it's no different for Qiyana.
Kai'sa is a lot more neutral than what you might think. Her new story "Monstrous" perfectly portrays that. I won't spoil it because it's not even officially released and it's very good so if you want more on Kai'sa's murky morality, read that on the wiki.
Vayne is an example of a "monsters make other monsters" story. Sure, yeah Vayne purges evil, if you consider evil as anyone or anything that uses magic in whatever way, even if it's used to help others. It doesn't matter who you are, it doesn't matter how close you are to Vayne, it doesn't matter how you use your "dark" magic, it doesn't matter if you're good, Vayne considers you evil, and so you will be killed. While Vayne has dedicated her life to hunt down Evelynn, she kills any magical creatures along the way, and her methods are pretty brutal, and it's made explicitly clear that she very much enjoys murdering magical creatures, she's extremely sadistic if I'm being honest, her short story makes that clear.
Now as for Pyke, I really wouldn't consider him full on the worst assassin (in terms of morality) if I'm being honest. The swimming city gave him powers and pretty much turned him into a madman who just wants revenge. His list isn't even exclusively filled with captains, the swimming city communicates with him through that list and gives him the names of the people he has to kill, and it's implied that they're not always captains. He's completely insane and is only fulfilling the wants of the swimming city, not his own, he's more or less a pawn for greater forces. He realizes this, but he really just doesn't care.