Annoying Doesn't Always Mean Broken
I think when it comes down to it, we call champions "broken", "overpowered", or "overloaded" because they're so annoying to fight. Just because a champion is annoying, doesn't mean they're actually powerful, but there is always the possibility of that. Even if a champion isn't overpowered or anything, being unfun to fight is just as big a problem. People play this game for fun, right? It's hard to have fun when fighting an annoying champion, like for me I have to say that
,
, and
are all very annoying champions to fight. And while I tend not to think of the champions as overpowered, I think they should have changes to be less annoying for those fighting them. Even if it's fun or flashy or $LCSBIGPLAYS$ for one person, doesn't mean it's fun for the other.
What I'm trying to get at is that the community should know when a champion is actually broken, or if they're just annoying. And for Riot too, so they know that they don't necessarily have to nerf a champion that's annoying, but change their kit to be less annoying through mini-reworks like
and
. (OK, maybe Shyv was a bad example of being less annoying, but the point still stands)

is the most annoying thing ever, but he's not broken I can tell you that much
get trashed patch after patch after patch for being "annoying" and other champions like
will get one patch of slight nerfs with compensation buffs that make the nerfs almost meaningless.
is a broken champion. His kit doesn't have good synergy with itself and his gameplay is very low quality against a lot of the other roster. Normally a low quality kit is fine, but it needs to work together like
.
is currently a broken champion because he is an assassin that can effectively build as an off tank bruiser and still one shot as an assassin while being able to be immune to CC, hence why riot is removing the immunity from him.
are annoying champions because their kits flow very well within themselves and have very good synergy and a high level of quality play. The only real argument I can see is Riven's animation canceling being broken, but riot has stated the like it on her.
she's not op, but she can miss 5000 qs and then not get punished, and then the second she lands one its like BOOM.
are annoying but useless...