As far as I can tell,
has everything a champion would ever need to be an adc, except for, of course, ad. Which should make him the perfect choice for when you are playing adc but your team is full ad. So what is holding him back?
Probably just the fact that no matter how much you spend on AD for him you would have been more effective with AP. Now if you mean sending him bot with a support and building AP then sure, I've done that several times. He's quite good in botlane against some matchups.
Take ADC Azir in to ranked and tell us how it goes. Good luck #lol
One thing i did notice when playing against him once as an ad (ya it actually happened) is that few people truly understand what your doing a/o how to play around it. So my support was paralyzed in lane the entire time. R.I.P. but it wasn't that bad. Although if someone understands you they can shut you down hard if they walk out of your soldiers then continue forcing the fight, which is way easier to do with 2 people than 1 in midlane.
Just watched someone playing AD Azir for funsies so maybe he wasn't building it correctly but this is what I noticed:
Your W scales off of AP so building AD doesn't help it damage wise. You have to use W to use Q and E but if you have your sand soldiers up, you can't AA. Without the damage, the sand soldiers' main purpose becomes just for dashing. The only other skill that you're left with is your R, which again scales with AP, so you're mainly using it for utility.
I have no idea why his secondary role is adc, is it the consistent damage thing with his soldiers?
Far too big windows of vulnerability for a 2v2 lane. He's going to get completely zoned off the wave whenever his Q isn't available.
Sheep. Bot lane carry can be played by a bunch of nonadc champions. 
(AP) 
