I'm guessing at least Teemo is on this list (despite that his shrooms are toxic, pun intended), but I'm also guessing Ashe, Singed, Garen, Irelia, and maybe a few other early ones. Simply put, certain Champions are just too difficult to rework without either destroying their identity, pissing people off, or something else.
Is it due to how much of an icon some of them are?
Sunfield2 votesThere is no icon that cannot be reworked. But Im guessing whatever happens, shrooms are here to stay
IAmNeverViable1 voteshecarim because he rely on movement speed but riot can't really fix his numbers without killing the fast pony.
darkdill1 votesHecarim is fine. He if anything is very good design.
Ashe and Singed, on the other hand? Boring gameplay.
IAmNeverViable1 votesI meant his w and e. It has such a long cd.
darkdill2 votesIntentional CDs. Makes you not just spam them and have to time them right, even if you get 40% CDR.
And you seem to be missing the point of this thread.
Hoi Im Temmo1 votesSinged isnt boring, tag is always fun ;D
Seriously though, I love to play singed. pls no judge me.
Sunfield1 votesHow would that make him fit for a rework?
Hoi Im Temmo1 votesRiot nerfed Teemo down to fair, then people complained NOT becasue he was unfair, but becasue it was Teemo...so they nerfed him more. but his mushrooms still existed, so people still complained. So they nerfed him again. At this point, even LCS players considered him a troll pick (see S3, TSM playing teemo for fun, because it didnt matter anyway) - but shrooms STILL existed, so they nerfed TWO MORE TIMES THIS SEASON.
Teemo is one of my FAVORITE champions (those of you hwo dont like, I dont care. Teemo is fun and awesome) and yet, I have been reported for simply picking him because of how bad Riot has murdered him. I honestly would love a Teemo rework, casue even if I wanted to, my team would not let me play him as he is now.
Kazellion21 votesCan't fix teemo by numbers tweaks without changing how 
liandries works so teemo is screwed for the moment.
Hoi Im Temmo1 votesWhile that is true...teemo has become more item reliant than jax. You practically need to have liandrys, crystal scepter, deathcap, and probably nashors tooth all at the same time to truely be effective - but at that point, you are either dominating the other team regardless, and it doesnt matter....or are so far behind you wont get to a third item the whole game.
AliceInMadness1 votesId say any champion that relies on spell interaction exclusively to be useful because changing one spell means changing the whoe kit massively and therefore their identity and the unrecycled* old ones
e.g. Orianna, Syndra, Cassiopeia, Morgana, Vayne, Riven, Zyra, Yorick, Ryze, Singed, Karthus and Old Karma( remember the shitstorm that followed her rework? its why they are so cautious with the current reworks and releasing them so early in the pbe)
*the ones that have the most uniques kits in their entriety, for example Braum is recycled because he has essentially karmas poke ability, Lee sin's shield, ysuo's wall and nami's ultimate but all of it in a modified way(instead of a shield he gives resistances fr example, Q scales off hp instead of ap) and skarners passive. He could be easily reworked because his only iconic thing is his moustache.