Can champion design cause player toxicity?

This questions keeps popping up in my mind more and more now that I stumbled about it while writing something else.

And I'm not just talking about players that already have a toxic mindset. Those usually gather around the current "free ELO/FotM" champions, thinking they get easy wins, get stomped hard because an OP champ is actually not OP when you can't play him mostly and get super rage-y. No, I'm talking about a champion design that actually MAKES people toxic.

In more than four years of league now, I have seen many champions be strong, or weak, be dominant, or outclassed. Usually the toxic FotM crow moves along with the champs that are currently strong, but some champions seem to have a permanent playerbase of toxic players. And since the only thing they have in common is that they are playing the same champ, so it might have to do something with that after all.

And if it does, shouldn't Riot try to rework those champions first? After all, they seemingly do EVERYTHING to battle toxic behavior, even it that means totally ruining Solo-Ranked. Because nothing prevents toxicity more than being flamed down by a group of four premades, AMIRITE?

Those are the five from my personal, subjective experience, when I try to look back at the last years and not just at the recent months.

But what's even more interesting... couldn't there also be champion design that could encourage positive behavior? I mean, I have yet to meet a toxic Nami player- or rather, meet a constant flow of toxic nami players. They're usually so nice (But so, so, so scary when they snap. They share that with the Raka-Players. I guess when you literally kill yourself to keep your team alive and they still blame you, that's not good for one's nerves...). But is that even possible beyond support-champions?

So many questions... and so little brain capacity to answer them because it is 5:30 AM here. Boards, take over please, maybe your deprived hive mind can find answers to these questions...

EDIT: Fizz added to list.