Got to do 80% more damage on every attack after buying one and a half items (With no actual AD on them BTW) I'd view it as a "defining part of my identity" too. It's not. It's stats. Free stats.
His identity is a wuxia style wind samurai who flashes around the battlefield like, well... the wind. Free stats are NOT an identity and they shouldn't be. Would we make a champion who's concept was that he was really rich so he started the game with 2000 extra gold? No. Even if that would make sense in-character. It's dumb and broken. Yasuo gets a hideous chunk of stats that other champions must pay for... for free. Crit from his passive, health from his shield, and armor pen from his ult. That's ignoring the huge movement boost his dashes provide.
An identity is how a champion FEELS. Yasuo could have other mechanics to make him more bursty or more able to do damage. Getting extra stats for building his items isn't a good way to go about it. That just means that he's effectively got more gold worth of stats than other champions who are going even with him in gold. His passive may as well be "Yasuo gets 50% more gold from all sources until he has gained 300 gold this way". That's a crappy passive, isn't it? Well it's basically what giving him something other people have to pay gold for for free is... and it's NOT part of his identity. It might be more appropriate if Yasuo was a con man who bilked the shopkeeper or something. New passive for TF maybe?