You see the issue here is you mistake the soldiers attacks for AAs. Perhaps i shouldnt use this wording either.
The soldiers attacks replace Azirs autos when they are in range yes, but they deal damage in an AOE line along their spear.
Becuase it is a spell not a true AA (becuase it can hit multiple things) Rylais applies the AOE duration slow.
The problem with Rylais on Azir is that it gives Azir a false sense of security.
It actually gimps his DPS compared to other stuff he could get, and it stops melees from getting ti him yes, but they were never really a threat to him.
Assassins are a threat to him, and slows don't cut it with assasins.
Long story short, he has been balanced around having this slow that he actually doesn't need as much as he thinks.