The first one that comes to mind for me is Evelynn; her current kit is very thematically bizarre and exists in a way that CANNOT be allowed to be strong. I'll go point by point.
In theory, Eve is supposed to be a shadowy temptress who kills those who she ensnares, but in game, that's not what she is at all. She's invisible all the time (a very odd idea for a seductress), and completely unsubtle in combat: she runs right at you while impaling you constantly and clawing at your face.
Her gameplay is problematic because all of her abilities are point and click (unless you count her ult, which is a technically skillshot in the most literal sense); this isn't an issue on its own (Vladimir, Pantheon, and others are in the same boat), but then it comes to her passive. Limitless free stealth is simply so strong that it consumes an enormous portion of her power budget, and so her other skills really have to pay the price. She can't have burst (nobody wants continuous Rengar ult), so she usually plays as an AoE damage tank, but there are other champions who do that a lot better (coughDariuscough), and this build wastes the stealth that contains so much of her power. It's also completely out of character; why is a stealthy seductress trying to get all up in your face and absorb all your damage?
Evelynn's theme wants her to be an assassin/mage; in all honesty, it wants her to be Ahri. In order to keep her okay to keep her stealthy angle, but the passive will definitely have to go. Too much of her power is invested in it, and if she's going to be a viable assassin, she can't have that kind of power drain.
Obviously, I don't work for champion design, but if I had to rework Evelynn, I'd probably do something like this.
Passive:
Love Is Blind
Whenever Evelynn hits an enemy with an ability, that unit loses vision of her for one second. (They cannot see her with wards, their own vision, minions, or towers.) This is not stealth, and so is not countered by true sight. Other enemies can still see her but this vision is not shared with the blinded enemy. This ability will drop minion aggro (although not tower aggro, since none of her abilities work on towers). Enemy champions hit by Evelynn's abiltiies are immune to the passive for two seconds.
Q
Death's Kiss
Evelynn fires a linear colliding skillshot that deals 80/110/140/170/200 (+50% AP). This ability deals 50% increased damage to champions affected by Love Is Blind.
W
Siren Song
Evelynn deals 50/70/90/110/130 (+60% AP) damage to each enemy unit in a small radius around her. Enemies affected by Love Is Blind are charmed for .5/.75/1/1.25/1.5 seconds.
E
Widowmaker
Evelynn's next basic attack deals magic damage equal to 6/7/8/9/10% of its target's missing health to all enemy units near his target.
R
Love-Hate Relationship
Passive: Evelynn recieves 30/40/50% increased movement speed towards enemies affected by Love Is Blind.
Active: Evelynn marks a target. For the next 9 seconds, Evelynn deals 20/25/30% increased damage to that target and takes 40/45/50% reduced damage and crowd control duration from other non-tower sources.
The passive takes her somewhat oppressive passive and puts it into a more combat-oriented stealth mechanic, bringing it into a more subtle style. Death's Kiss is a very straightforward damage spell, but the interaction with her passive makes it more interesting; do you Q first for the crowd control or W first for the extra damage? You could also run the risk of trying to get into melee range, applying the passive with the E to get both the extra damage and CC from the W and Q. The ult is a less irritating version of Poppy's ultimate (which is soon to be an empty niche, hooray!); it's the assassin-y bit of her kit without all the trolly tower-diving and impossible-to-killiness that it brings with it. Anyway, this is just something I came up with for fun.