Raise Azir Q cooldown significantly, especially early game
At least you can go around his soldiers... oh wait you can't because Q is up every time he throws them down so you have no real time for a counterattack if you can't tank them Q + 2-3 autoattacks (assuming he is playing smart).
Especially vs squishy mages, he's like release orianna 2.0 in zoning if you can't poke better than him, at longer range, sustainably, and over minions, while also having all-in potential beyond that poke.
You walk up to CS. He presses W and you eat an auto to the face. You can a: run and eat a Q+auto to the face or b: try to engage and eat a Q+several autos to the face, while he casually walks away from you. Even if you managed to get an ability onto him, he will have done far more damage. Though even bruisers have plenty of problems vs him too, being melee and all.
If you raise his Q cooldown, he can still drop soldiers down a ton but now you have a stronger window to counter-engage him, because if he waits for his Q to be back up he will miss CS meanwhile you can CS freely, and if he doesn't wait you have a proper chance to actually fight him without him just dumping soldiers back onto you with Q after you bypass them