I like this prompt.
I think it would be too strong, though, due to the fact that his soldiers already deal some seriously potent numbers on the target. If they were weaker, it would force Azir to build Nashor's Tooth, which we all know being forced to build an item for damage can be kind of lame. Furthermore, it would open up the question of "Should his Soldiers proc other item passives?" and that can be extremely uneasy ground to walk on. He also scales off of Nashor's stats, so it would also become even more cost-effective on him.
I don't think Azir's issue is damage - he does some great damage already. Rather, I think his issue lies in the remaining bugs he has on top of his lack of survivability throughout the game. He requires a good chunk of mana to lane effectively, though not as bad as some others, but he's considerably squishy given the range he has to be in to deal optimal damage. He requires a decent level of skill not to be abused by his opponents too - it's easy for him to overextend with his soldiers and sometimes trying to finish off a target can be suicidal.
That said, when he did have survivability in the form of his E's old shield, he was extremely powerful and oppressive. What I think he needs, IF he needs anything (he's quite potent in professional play), is to improve his survivability/sustainability in lane to at least allow him a better chance into the midgame-lategame where he excels. Given how laning presence and power for most of his competition has improved, I think he could use the attention.