The problem with the Azir nerfs is inevitably that he needs the damage, because he's not a utility mage. He has utility, but to kill people not to lock them down.
In this sense, he is already so difficult to micro manage his soldiers that constant damage reduction to said soldiers just makes him into a much weaker and more gimmicky Orianna. Case in point, if you were an ADC (who also have slows and disengages), but now you had to reload your weapon and every time you attacked it was a skill shot and then they started to reduce your damage... where would you be?
Plus, he's supposed to be a zoning mage. How is he going to zone now? They nerfed his overall damage last time and buffed Q saying it would help even him out more. Now it's straight nerfs all the way around.
So, yeah he will still be functional and playable... but why would you play a character that you have to micro manage that much if the benefits aren't going to be very good or in fact less than another character in the same role?
Azir = Micromanaged magic adc. He does not root, he does not stun. The most he has on him is a slow and a good disengage that comes in handy in team fights if you are almost right on top of the people you are fighting already. I mained him for a lot of s4 (most games played) with a decent win rate. I'm not high elo, but I know it's bad when they expect you to stand there longer to kill someone when you are a squishy mage and you have to move your spells (soldiers) around just to damage. Can't even build tanky anymore and expect to have that damage.
Until they figure out what they are doing with Azir I'm not playing him anymore. He won't be unusable, or broken, but his consistency is going to tank and he just won't be fun to play anymore (not that we got a lot of time to try him with no bugs before the nerf bat started swinging at his legs).