Azir is meant to be weak early on, he becomes a powerhouse late game. That is kinda the point. He becomes even more threatening than an ADC since he is basically the AP version of one ON top of having a lot of mobility, safety and hard CC.
Not to mention Azir is meant to be a very hard to play champ since if he is played to his full potential he is one of the strongest champs in the entire game.
Also how is it expensive? Or rather any different than any other AP? Everyone gets Rabadons so that part of what you said is purely stupid. Everyone gets Sorc or Lucidity so again, irrelevant and kinda funny you would even say it. A good amount of AP get Rylai due to its sticking power and added bulkiness. Of course its going to cost more than say Void Staff or Ludens when it gives roughly the same AP but also a large amount of health, as well as its slow on every spell..... As for Nashors, its the same as all the other AP items, its also a strong one for champs like Teemo/Kayle/Azir because you are adding your AP to auto attacks, thats pretty powerful....and again it gives the same AP as just about any other AP item.
So I am sorry but explain to me why he is appearently expensive when half what you said everyone else gets, and the other half of what you said costs about the same as well as gives same stats if not more as the rest? Like not trying to be rude, but you made a pretty bad case, if not borderline stupid one.