Here's why I disagree.
TL;DR: Yasuo, Riven, and Lee Sin are strong. They are allowed to be strong because they're not at Azir's levels of overloaded. If Azir is strong and that player is good at him then there is not one single reason to not pick Azir. Azir lacks bad matchups that scale well into late game and is a late game monster. Azir engages and disengages multiple targets at once while providing an impassible wall that allies can walk through. Azir can shut down entire sections of the fight with his soldiers, ult, and passive. Azir provides a staging point for any siege, a rallying point for any siege, a DPS source for any fight, an AOE source for any fight, can keep himself safe and at a distance, and as a result Azir can make or break entire teams. No other champion in the game can provide as much as Azir, as safely as Azir, and as reliably as Azir, provided Azir is a strong character.
It's not the matchups that make azir great, it's the fact that if he's strong he's useful ALWAYS and forever.
Unless Azir happened to get stomped he could, as I said, do everything your team needed in a damage dealer.
Yasuo and Riven basically have to all in to get anything done, Riven is mobile for sure but she can only fight from melee range, which puts her at risk.
Yasuo's mobility requires enemies to work, meaning he has to go in or have someone he hasn't hit yet to get out with a piddly little dash. He has a single ranged attack in order to do anything and happens to have a wind wall to help shut down ranged harass so he can try to get in melee safer. Still requires himself to be in melee range.
Lee Sin has mobility sure, but that mobility requires him to have a ward or ally, the mainly reliable of which takes a slot that makes it so he needs to keep wards on his person, or he has to hit an enemy with a skillshot.
Compare to Azir, who can make his own mobility and has self peel that shuts down all but one type of mobility. Who has sustained damage similar to an adc while dealing magical damage which forces the enemy to build MR and AD, thus splitting their resistances (all mages do this, but Azir can pump out numbers like nobody's business from a safe distance away). Azir, who can create immovable objects and a flippin turret to secure an area. Azir, who can clear lanes entirely safely at all stages of the game while getting off pretty much free and safe poke as well.
Don't get me wrong, none of the champions you mentioned are weak, but I think you're mixing overloaded with hyper mobility.
Here's what Yas has.
-DPS/Burst damage from his crits
-Conditional mobility
-Conditional knockup and conditional suspend
-Self protection from about a single source of damage (give or take another depending on how much you hit him until the shield goes away or how strong your hit is)
-The ability to eliminate ranged abilities from the game, which does not bother melee attacks in any way shape or form and thus essentially exists to get Yas into melee so he can do his thing or to say 'no ranged people, you cannot hit me from safety'
-Passive double crit chance.
What Yasuo lacks.
-Any way to really engage or disengage for his team, this is because the tornado requires Yasuo to have targets. Azir has this.
-Any way to deal with melee attackers who are flat out stronger than him at murder, Yas can't run without a minion wave. Azir can do this.
-Poke or siege of any kind, he's melee so he has to go basically balls deep to do anything to anyone who isn't a tank. Very dangerous.
-No resource, limits his build path.
Now, don't get me wrong again, his ult is pretty good at getting him into range so he can do his thing and start shredding folks, but it's still conditional and still throws him into melee range with no way out besides the murder of him or the enemy. Also his crit passive, no matter how much you and everyone else might hate it, forces Yasuo to build critical hit damage. He needs to get online earlier than an ADC because he's melee, but with his kit if the man was allowed to not force a few of his items into crit items he'd be so much more annoying to deal with.
Plus Yasuo's abilities all scale horribly with CDR besides his Windwall, thus further making the player want to build in a certain way in order to try and maximize his kit. This makes it so Windwall is a much higher value of an ability to use and thus super important if it's down.
See Tank Yasuo for details.
Riven:
Pros:
-High mobility through 4 dashes
-Small AOE CC
-High damage
-Big, short lived, shield
-Execute AOE skillshot
-AD steroid.
-No Resource
Cons:
-Gets shutdown hard by anyone who happens to be better at bullying than her. (this happens with all melee champs though since they can't really farm safely outside of the few with long range spammable attacks, like mundo.)
-Only way to deal with poke is her dash shield
-All in only. If she's trying to kill you, she's going to blow everything except maybe her shield dash to do it.
-Only ranged skill is an ultimate
-No resource, meaning no tear items and items that give mana are less efficient on her.
Basically, she has to go on, which puts her at massive risk. She has only utility on one skill which is a melee range stun and no real tools to deal with coordinated efforts to eliminate her. She lives and dies by her ability to dash for that shield, and without that shield she's incredibly squishy since she has to build AD to be a threat.
Lee Sin.
Pros:
-Has Peel in his ultimate and his slow
-Can engage with his ultimate if he performs it perfectly
-High damage early on, kinda meh damage later on
-Self sustain (provided he can remain in combat) for both energy and hp
-Small shields
-2 dashes, one of which being point and click to allies and the other being a skillshot
-Energy champion with efficient energy regeneration
Good at getting in, good at getting out provided he kept a ward around. Not super hard to do but again it limits what Lee sin must have in his item and trinket slots. Decent engage provided the stars align and good damage scalings.
Cons:
-Energy based champion, he has a limited pool to work with and in order to replenish that pool he has to limit his casting and auto attack which is risky in a fight. Unless he builds tanky of course but if he's doing that he's not going to oneshot you when you're full build.
-No zone control, Lee's only zone control is the fact he's there, that's not much.
-Engage and Disengage need the stars to align to be useful against more than one or two people. Lee can pick on average 1-2 people, Azir ult could pick your entire team. Granted that's an unfair comparison since Azir is overloaded AF but still.
-Is melee, despite his mobility he still gets most of his damage off from being melee.
-Lacks sustained damage, Lee is entirely CD reliant and lacks powerful steroids for his basic attacks, unlike Riven or Yasuo or Azir for example.
Basically, Lee can get his job done fast and relatively safe but he doesn't have much after that. Lee sin, once he blows his load, is a glorified melee creep until he gets his cooldowns back. Cooldowns aren't long no but there are better options for just straight up deleting a person safely.
All of the people you mentioned are strong, but they lack the utility combined with the constant damage potential that Azir has.
They can be strong without being the end all be all of anything ever. Azir, if he's strong, can do everything and anything with zero weaknesses provided the person playing him is doing a good job. I repeat, Azir's only remote weakness is he isn't beefy.
Sorry for the wall of text. If I said anything wrong then feel free to comment, and I genuinely enjoy discussing ideas so I would love it.
is almost forgotten, only his mains are playing him, yet they barely win 42% of their games.
Meanwhile this full load of BS champ 
with unnecessary Q M.S steroid and 3 damage dealing dashes which you can use up to 3 seconds between each is on 54.6% win rate compared to her pick rate 18%.
37 and dropping hgnngngngh
