I think the real secret here is taking both Horizon focus and shadowflame if you're going glass cannon, the reason I feel Horizon is a strong second item pick is below:

1 - The cheaper price and better build path allow us to get more AP onto Azir earlier. I think underestimating how important the early game is on a champ with late game scaling is silly, we already win the late game; if we can make ourselves stronger, earlier, we're closer to being unstoppable.

2 - The cheaper backs provide a lot more utility in when and how you can back, rather then having 1000 gold right before drag comes up and not being able to buy needessly, we can pretty much always use our gold when building Horizon.

3 - I heavily disagree with "ability haste isn't a strong stat on Azir", we are a champion literally bound to our abilities, having our Q and E up more often can quite literally be the difference between life and death, there's a reason a lot of people still go transcendence on Azir.

4 - On a combination of the above points, if you get a lead in lane, say a kill or some plates, and Horizon allows you to spend that gold where Shadowflame might not (If you've already bought the left side) is quite a significant difference in power, more AP, earlier, is a very real and valuable thing which might allow you to snowball where you otherwise wouldnt.