I would only pick Azir for
His ultimate.
Generally, if I want a god tier monster late-game, like you want Azir to be, I pick these champions:

Taking his AOE away from his soldiers auto attacking will not only solve problems in the LCS, it will remove him as a whole from Soloque and general outside of LCS play. By the way, because the forums are so hyped up on win ratios as if it was a physical god that at last shown himself after thousands of years of trolling, he has the lowest win rate in the game. Below Urgot and Ryze.
Now let's talk outside of the win rate:
Do you want long ranged DPS with a stun/knock up that includes magic damage?
Would you like mobility on the side as well as safety? 
Do you want to go in and deal magic damage, while also being an engager?
Don't want magic damage but also being capable of the same thing without running out of resources? 
Do you want to stop block enemy
from carrying his adc into safety?
Do you basically want an Azir ult without displacement? 
Do you want an ADC like champion that does consistent damage until death, as well as having an engaging tool? 
Why would you EVER pick this piece of shit champion? "But the problem is that, he has like. You know. One of the most overloaded kits in the game with extreme safety, and a free "Fuck your gank" token every 2 minutes. He also has one of the highest DPS's in the game, capable of competing with
in DPS, how do you expect us to make this champion balanced?
"Uh, you know the game is revolved around skill cap, right? I, as a Riot employee, a part of the balancing team, believe in this statement. This champion is much harder to play, and therefore should also be better than other champions. Isn't that right, Thresh?"
"
"Yeah, just look at Janna, Just sitting in MY lane. Like she owns it, like she knows me. Like she thinks she is better than me, I'LL KILL YOU."
". . . . . . . . . . . . . . . . . . ."
"Yeah, actually. Now that you say it, Thresh. Janna is kind of getting out of control, I mean she has a fucking shield. How OP is that!? Anyways, we will be nerfing her for the next 5 patches, shifting her strength without logical reasoning as for why Janna is a strong support. Are you looking at us, Lulu and Sona?"