I have no issues of having AA being the strongest form of damage, because it's the only forms of damage that has typically the shortest "CD" if we don't consider the 0 CD oddballs like Yasuo, it has no cost whatsoever, and will never miss within normal circumstances, hence augmenting it with AD items and whatever makes strong and reliable source of damage.
So that is fine, at least when it comes to LATE GAME damage, after when the AA has been seriously boosted by items.
What is NOT fine, is as briefly touched on, the fact the game is heavily skewed towards making AA FAR more appealing than any other forms of damage (think the assassin rework that delayed assassin burst for the supposed counterplay reasons, but then leave crit AA 1shots, which is definitely far more problematic than an assassin blowing someone instantly because at least the latter rotated their skills into CD, completely scot free), with things like the removal of spell vamp but keep lifesteal, AD items being far more diverse than the AP component with all kinds of unique procs and whatnot, late game ADCs spike "late game" way too early, crit items being way too cheap and scale way too well or otherwise the continuously borked crit balance, and things like that.
I wouldn't say the problem is rooted in AA itself, per se.