Ahri is not considered to be an assassin by Riot.
LeBlanc's Distortion is only a small portion of her damage. Much more of it is single target than non. Also, it's not like Ezreal's E where it makes sense to fire off a homing shot after you've moved. How would her W deal single target damage?
If it dealt no damage at all, she would ONLY use it as an escape, and that's worse design than giving her AOE.
Zed was the first attempt to give a mid lane assassin some utility. So he got wave clear so he could split push.
Talon and Katarina are THE team fighting assassins. They are significantly worse at CSing and are much less safe with their single target patterns than other assassins to compensate. Compare how Kat kills someone to how Akali kills someone and it's very very obvious.
Yasuo was created to be an assassin who plays bot lane with a support. He was Riot's first attempt to break the marksman/support meta, and his highest win rate was indeed bot for a while. Because of that, Yasuo needs to be able to clear waves to help prevent him from getting three man dived.
Also the assassin who has the lowest AOE damage, Shaco, never gets built tank. So your third point isn't exactly strong. What makes assassins get built tanky (the fact that you didn't include Elise in that list is shocking and makes me question how long you've actually been playing the game if you don't consider Elise to be a tank assassin) is their utility. Assassins have high base damage by necessity, to give them the edge in trading so that they can fulfill their fantasy of getting kills even before they have items built. Assassins that have powerful crowd control like Ekko, Rengar and Elise therefore can kill people without building damage, so they build tank to get multiple uses of their crowd control off in a single fight.