I keep seeing this so I am going to be pretty comprehensive.
You are missing out on a lot.
You are missing out that every caster who has one can "hold their stun". You are missing that Annie's stun has an effective CD like other mages who have stuns and other hard CC abilities, but those other mages can CC from not only a longer range, but with an additional strength of having it always up, and can use other spell without putting it on cooldown. Nor do they have to put other spells on cooldown to remove their CC's cooldown.
You are missing out on champion damage potential and understanding it. You are missing that champions can regularly remove half an opponent's health in a rotation.
You are missing out on understanding that champions' capability to take down other champions go up significantly at Level 6 and it is not unexpected to do so and "delete" (100 to 0) enemy champions in an engagement.
You are missing out on the fact that champions can all-in and and 100 to 0 before Level 6. You are missing out on the fact that champions can all-in and 100 to 0 the enemy laner at Level 1.
You are missing out on the fact that Annie is a short range mage and the most linear champion in the game, meaning that she has inferior harassment capabilities and that she is extremely choreographed and predictable while also lacking the tools, or capabilities that other champions can use to beat their laner or to play the map strategically.
a champ that can just save flash hold a stun and instantly delete your adc with no problems.
You are missing that every champion in the game can flash engage while engaging champions, who are numerous, are not flash dependent like Annie is and that ADC are the most vulnerable, and easiest to take-down role in the game by a large margin and can be quickly taken out by the majority of the champions in the game.
So no, Annie is not a problem. Let alone a major one.