For Azir specifically, I think his biggest sticking point is just how little mana he needs to use when zoning or clearing waves. Compare him to other control mages like
or 
But it's not that Azir is problematic, it's that other mages just are not up to par in kit anymore.
- small AoEs compared to others, needs to rank up both W AND E before he can clear waves. E is kind of a throwaway spell, ultimate is pretty "meh".
- Suppression only stops
and doesn't prevent
, which is his only defining feature.
- His Q and ult are fine, but his Bulwark and Righteous Gust are pretty obsolete. Staggering mana costs AND HE'S MELEE. There are too many mids (especially assassins) that can just abuse his melee range and high mana costs to absolutely no end.
- he pretty much just dies. The game is so packed with front-loaded damage, even from.items, that he can't even position to deal damage before he's dead. He either needs way more damage, needs tank base stats or needs to be able to move in his passive. Either of the 3 would work.
- he needs WAY too many stats to do what he does. There aren't even enough items for him to have AP, health, Mana, Mana Regen, Armor, Cooldown Reduction AND Magic Resist. He needs a broader range of very high stats than any champ in the game. He needs to gain them in his ult or something.
- he was never more than mediocre, even upon release. But a wider knockback would go a long way