Xaritscin, you're pretty much just wrong. Not trying to be a dick, but you're trying to say, definitively, that Kassadin is underpowered and should be rebalanced/reworked/etc. Basically everyone else, either from playing him, playing against him or watching games with him being played are saying that this is not the case. Please accept the possibility that you might be wrong about him being underpowered.
Kassadin's RQE combo will not result in a kill on someone at full health unless Kassadin is completely fed, higher level, or they build absolutely no defense and are naturally squishy. Kassadin is not a full-health burster. He whittles you down, bit by bit, then he pounces. That, or he shows up towards the end of a team fight to clean up. He has considerable burst, but it's all about the time leading up to the burst that matters, not the burst itself. Positioning is absolutely important considering he does not build to supplement his melee attacks (although those can be useful with his w, they are just dangerous), so he usually only goes in when he can guarantee that he'll also get back out.
If you have played other assassins, you should know that very few can burst someone down from full unless one of those situations are met. Assassins are terrifying because they stop you from doing pretty much anything, constantly chasing you down and doing absurd damage as long as they stick on you. Only assassin champions like LeBlanc (who was rebalanced so it's less of a case now) put you in danger of immediate death when you see her, and that's still only if you haven't built defense or are naturally squishy.
That said, if you're an assassin and you're jumping, alone, onto anyone that can survive your burst and stun you after you silence them... you're doing it wrong. You listed 2 tanky dps champions who are naturally resilient against assassins (so you're saying, "Kassadin can't burst down his counterpicks!") and Master Yi who is an AD assassin, meaning that all he requires to kill you is to get close, which is necessary for Kassadin. So again, you're right. Kassadin going against them is a bad idea. That's because he is not good against them, not because he doesn't have the power required to be an assassin.
You also won't see those types of champions mid unless you're horribly unlucky (or lucky, considering it should allow your other lanes/jungle some advantages).