It depends on what point of view you're coming from
Many people argue that assassins shouldn't be in the game, but I don't feel passionately about that one way or another.
I don't think a champion is cancerous when they kill a lot of people. We know this game isn't all about KDA. However it never feels good to die, and that's the whole reason the assassin class exists, to deal high amounts of damage. That's it.
It's easier to blame them instead of taking responsibility for a silly mistake you made, and that's almost all of the deaths that happen against assassins, or at least that's how it used to be. Now it's hard to catch these champions, and when you do they sustain damage quite well.
I believe assassins get out of hand when we try to make them a more reliable pick. I can play against a fed feast or famine champion. I know what's going to happen when they hit their 3rd kill, and really we all should know. Even so, there's a reason those types of champions thrived in low ELO.
Assassins are cheesy champions by nature. They rely on getting kills early game so they can run around the map taking out other champions who are out of position, standing near an unwarded bush, or split pushing alone. They should thrive on disorganized teams. They should never be a huge threat outside of 1v1 or 1v2 situations.
A healthy assassin should have high mobility, deal a lot of damage, and have little to no CC. Any sort of lockdown, silence, or escape is toxic when an assassin has it.
They also need to be quite squishy so that any sort of lockdown messes them up. That's the trade that needs to be made for the high mobility and damage. When you add escapes, hard CC, or any sort of reliability into an assassin's kit, they become too oppressive.
If an assassin is building defensive stats then they should be significantly punished for doing that. That's the way it used to be, but now there aren't really anymore true glass canon assassins. Fiora got a rework, and even Yasuo builds Maw of Malmortius, Guardian Angel, and Sterak's Gage now.
Currently I would say Katarina, Kassadin, and Ahri fit the bill, but I believe that's more because of how mages aren't really at the center of the meta right now. AP assassins like Fizz and LeBlanc remain commonly picked and banned because their kits are problematic when you deal a lot of raw damage.
AD Assassins are even worse at the moment. Off the top of my head, I could only think of Shaco as the least problematic, and he's not all AD.