The problem with Azir is the same as tank assassins: bad MR itemization
Armor itemization for tanks:
Big-ticket HP+Armor items which give you a huge amount of effective HP vs physical damage.
Designed to counter AA-based dps carries.
MR itemization for tanks:
Always bought by the support and the aura doesn't stack, so it's often wasted stats
has wasted stats unless you're mundo or another self-healer.
doesn't have much HP, so it's not a great 1-item wonder, and its passive works vs burst, not dps.
Honorable mention:
Good vs AP burst, not so good vs dps
It's usually OK for MR to be weak
Because most AP champions are spellcasters. They have cooldowns, so MR has to be weak; if it's strong, they're useless.
Azir changes the paradigm
Azir brings marksman-level magic dps. Normal MR isn't sufficient against him. That's his problem.
This is also the problem with tank assassins (who, you'll notice, are all AP): MR itemization is designed to counter burst, not DPS. So if you build tank and use your base damages to do dps, you're much more effective.
The solution: New MR items!
As we covered earlier, we can't just buff MR, or we invalidate AP casters. So instead, we need a new type of MR item, the equivalent of Frozen Heart or Thornmail.
Some people will say "Locket is the MR version of FH." Well, kind of. FH reduces dps from aa-based champs, not AD casters. Locket reduces all magic damage. That means locket is equally effective vs AP marksmen and vs AP spellcasters, in which case we're back to the same problem, that strong MR itemization will invalidate AP casters.
We need a better way to counter-build Azir that doesn't stop an assassin from blowing me up. Tbh, I'm not sure what that item would look like. But that's what we need.
Edit for clarification
I don't think MR itemization is Azir's only problem. The point is that magic dps + safety is a problem because there's not an effective way to counterbuild Azir (or tank assassins).
Restated, if you could counterbuild Azir, his overloaded kit would not be as big of an issue, because a tank could dive him and lock him down long enough to kill him, instead of diving him and dying before anyone can follow up.
that basically will stack everytime you get hit by a spell making following spells weaker.