I'm sick of having friends leave this game because of 1 champion. I know if they just played ranked, and got the ability to ban unhealthy champions, they'd stay. It's just that they can't even get to level 30 because of how frustrating playing against Yasuo is.
You gain access to Draft pick as soon as you get 16 or so champs and I think it's level 18? Then you get to ban him all you want. Also take into consideration that champions like Yasuo are popular picks for smurfs, champions that snowball extremely hard and that, in lower elos/MMRs will seem unbeatable.
He simply lacks identity, because he's designed poorly. Honestly, whoever designed the champion, or let it's current iteration through to the live server, should be fired.
Except he doesn't lack identity? He's the Wandering Samurai with power over the wind of League. AKA: the weaboo bait of League. As swift as the wind, as unpredictable as the wind, and as destructive as the wind. His identity is pretty clear. Also, his designer is CertainlyT; you aren't the first to bitch about him. Just to give you even more of a reason to hate him, he also designed Kalista, Thresh, Darius, and Zyra. He's also thought to be the lead designer for the Warwick rework coming up soo.
Extremely High base damage
I wouldn't say extremely high, just high enough to get him through the first few levels. I blame Frozen Force Yasuo on TriForce being way too good of an item, and Fervor still being crazy. At level 1 it's a bit more than 55, on the lower half of the spectrum.
Unprecedented Mobility
You mean the short relatively short range dash (albeit, spammable) that is highly dependent on enemy/neutral mob position, let alone the actual presence of anything around to use as a dash. The only dash in the game that is completely interruptable by ALL CC. I repeat: ALL CC. All other dashes are only interrupted with airborne-related CC (knock-ups, knock-backs, knock-asides), other CC will wait for the dash to complete and then effect the target. That dash?
High Defensive Stats
Umm... you are aware that his MR has no growth? Only other melee champion that doesn't have MR growth is Kassadin, and that's because Kass gets his anti-magic damage shield pretty often. Yasuo has his shield, yes, and thus he has no MR minus the base MR he starts off with and the bonus MR he gets. Also, he only has a bit less than 25 base armor, and gets up to only 82.5 at level 18. Not extremely impressive at level 18, though in the upper half in the beginning of the game.
Arguably the best defensive skill in league of legends
Maybe try to not blow your big skills and ultimates when you aren't sure his Windwall is down? Maybe try and reposition? Maybe bait it out? Maybe get someone who's melee reliant and thus isn't effect at all by Windwall on your team?
The best bonus armor pen skill in the entire game
As far as I know, only four champions have armor pen in their kits: Yasuo, Kayle, Gangplank, and Darius. Gangplank has his barrels, Darius has his passive. Kayle has her passive. Yasuo's armor pen only effect his critical strikes as of 6.18 and is tacked onto his ultimate and is a buff that only lasts 17 seconds, which I admit has a short cooldown for an ultimate at ranks 2 and 3, but it's still an ultimate. The other three have their armor denial capabilities readily available most of the time.
Arguably the best personal shield in the game
A small shield that lasts 2 seconds that he has no control over. A shield that can be popped with an AA, waited for, and then proceeded with the actual damaging spells.
The best crit passive in the game.
There's really only four crit passives in the game: Yasuo, Tryndamere, Jhin, and Ashe. There really isn't much to compare with. Tryndamere's gives very early bullying power, Jhin's makes his trading before his crit items viable enough, and helps him kite, and increases his AD, Ashe's makes her deal more damage against slowed targets and doubles up on the slow when she crits, and Yasuo's simply doubles his crit rate at the price of losing some crit damage. They all have their strengths and weaknesses.
Regardless of what meta shift occurs, Yasuo will always be played, because he is inherently broken. Please take note that even when all other assassins are shelved, Yasuo still sees play.
Yasuo always sees play because he's extremely popular. He's popular because he's genuinely fun to play. He's popular because his fantasy/identity appeals to a very large base. Yasuo always sees play because he's flashy and rewarding to play once mastered. Also, Yasuo has barely seen play at all in the pro scene since last year, and if I'm not wrong, has not preformed excessively well. The last time I saw him in the LCS was Huni doing the Phantom Dancer + TriForce back when TriForce had crit, in the Spring Split. Yasuo has a very dedicated fanbase that will play him no matter what.