Some of them could use adjustments but honestly, champions with CC tend to rely on it. Annie without stuns would be horrifically outgunned and protracted, and you could basically just sit there and poke her from range. Nigh on her only hope would be flash and full rotation. After MR hit the scene, she'd be a backup tank with a backup-backup tank.
If they adjusted Tenacity instead, Irelia and Dr. Mundo would be scratching at the 50% mark which basically means they're never locked down for more than a full second, which would be absurd as they barrel down you. Irelia's already hard enough to stop with her passive, even after its nerf.
Rather, maybe range should be adjusted to hit 90% or 85% of total damage so as to balance out the fact that their early games tend to be safer. But even then, a lot of melee (I see Jax and Xin Zhao get shit on a lot) have disproportionate late games. In all the URF modes, Annie aside, I jump for joy at melee. Most of them wildly overcompensate with cooldowns and damage, and even the likes of Mortykaiser can get back at those pokes late-game.
You gotta think outside the box with melee. You're obviously at an inherent disadvantage in a direct confrontation until you reach them, and a lot of range comes with CC (in fact the most gross offenders for lack of CC are melee), so you have to find what your advantages are in that particular game. Xin Zhao is going to do really well in a game with middling mobility and slows, but he'll probably be doing really poorly if there's a tank to peel him away. On the other hand, even though the enemy team seems stacked with 5 mages/adc/assassins in some combo, Xin Zhao just has to task himself with dodging the most relevant of CC; unless they can pull mad distance, Merc's will push him pretty far into the enemy line and his ult will shake any formation pretty much instantly.
Some melee champions are some of the most satisfying to play and enjoy nearly-untouchable late-games. The non-SR game modes are almost always more highly encouraging of meta-breaking, thinking outside the box and reactionary builds (grabbing hard armor items on damage champs, for instance, as opposed to armor/dmg).
Also, healing was nerfed because late-game supports like Sona could sustain infinitely without some sort of limitation (even if, like Morello, it's largely only implied). CC is not so effective nor so simply classified.