I'm seriously confused to why Riot even gave him this little passive in the first place.
Well, I can explain the rationale behind it. The basic idea is that they didn't want him to only go after squishy targets. Most of our melee carries basically serve as pseudo-assassins, and they wanted Yasuo to do something different. They wanted to make it less reliable for him to do that when compared with assassins or assassin-like melee carries like Yi. By giving him a tool for going against tanks and bruisers, so that it could be made a bit harder for him to reliably reach a backline, and so that they could make him have slower burst when he reached it. It was intended as a mechanism to prevent him from being a pure assassin.
A difference between Yasuo and the assassins you mentioned is that they have less conditional, longer-ranged mobility, and they can deliver burst a lot quicker than he can without a setup. It makes them better at being opportunistic assassins than he is. They're significantly better at taking out someone who gets a bit separated from the team, or for quickly jumping in and blowing up a quick target. (Note: I'm not saying this makes them better than Yasuo. I'm just saying it's one specific thing they can do more much reliably than he can).
Now, because Yasuo doesn't have the same access to the backline that they do, and because he doesn't have the same level of immediate burst they do, there has to be some allowance for him dealing with a frontline. The allowance they chose was armor penetration. It works better against bruisers and tanks, so it lets them give him some power against them in exchange for some additional squishy-killing power they could have thrown in.
Tying it to his ult also serves as a gate of his power at the start of fights, particularly if he's split pushing. Instead of being like a Master Yi or Trynd who has the means to just jump on someone and throw all of their potential damage out, he has to get a bit of setup first. It also makes dueling him as a bruiser a bit easier when he's alone. He won't have his full power at the start of a fight, and if you can dodge the knockup, he won't get access to that power, which should hopefully give you enough time to take him out. It was also a means of forcing him to use his ult at some point during a fight, even if he can't get to the backline with it. If he doesn't ult, the frontline has a very good chance of just walking through him, so he sometimes has to choose to take a non-ideal knockup so that he can fight instead of being able to just throw down with the frontline and saving the ult for backline access.
Now, none of this is to say that it's the best option, or that it is working as intended. You could make a good argument that his access to it is still too high given his ult cooldown and range, and the setup is too easy for the reward when he's with teammates that have knockups. I'm not making any defense or criticism of his current balance state: I'm just explaining Riot's initial design thoughts, and why they do make some sense given what they wanted from him.