Ok so lets discuss this nerf:
This would make it so that Azir would have to get close to his enemies to deal the most damage, therefore encouraging him to get close. This nerf is the most "obvious" idea on how to implement this change.
Instead, however, what if we rephrase your idea to sound like this: Azir's soldiers get reduced attack speed the closer they are to him. What does this do? It makes it so that Azir has to maintain his distance to deal maximum damage. It means that if you manage to gapclose against him, he'll have a difficult time dealing with you.
This would be a much smarter nerf to him as it would encourage a play pattern of a long range auto attacker, instead of making him like every other champ that needs to get in your face to do damage.