Okay, as someone who has mained kassadin on and off ever since i picked him up in early season 1 or season 2 i've had the opportunity to play this sleeping beast at his peak when he was considered trash due to being as useful as a magikarp early game and during his highlight while being considered a completely broken champion with 0 counterplay. I have played against many kassadins and due to my experience with kass i always asked for lane against him so i could exploit his early game weakness and lack of ability to do anything against ranged AD champions (which i main, specifically tristana and vayne). I would say that while i'm no pro, i am certainly very familiar with this champion and this is my analysis:
Before the recent nerf, rift walk was the best ultimate in the game hands down. A low cooldown, high range blink with increasing damage per stack leading into a massive nuke of over 1k magic damage is absolutely beastly. To compensate, kassadin had only 2 ranged nuking abilities, a useless w ability, melee range, conditional wave clear, huge mana costs and an extremely weak early game. This was especially exploitable before flask and trinkets were introduced which allowed kassadin to handle early game pressure much more consistently and could allow him to survive even against his hardest counters such as pantheon.
Once kassadin became popular, a never ending stream of nerfs followed which gutted this champion like never before seen. His base damage is the lowest by far of any assassin, mediocre scaling, ult gated with extreme mana costs and longer cooldown period for resetting stacks, much weaker CC with completely removed silence and heavily nerfed force pulse slow. Even then, kassadin was still a strong champion due to having incredible mobility on his ult which allowed for excellent positioning in team fights and ganks from fog of war. Completely viable, still a strong pick in tournament level games and one of the best late game assassins with insane chasing potential.
However this last nerf with the reduced range on kassadins ultimate is by far the hardest nerf he could ever receive. Lowering his ultimate range by over 1/3rd is not just a simple nerf to his chasing , escaping and assassination potential, but a devastating nerf to how his kit functions in combat. For example, if a target is over a wall in a team fight, as kassadin you would blink over the wall, unload your combo and then either walk away or hourglass until your rift walk is available. Simple and effective way to unload your burst onto a target.
Now the main point here is that about half of your damage (especially if you have lichbane) is necessary to deal your maximum damage. If you get into melee range as needed, you will be completely unable to rift walk back over the wall to escape since you are now required to dry hump the wall before you can rift walk to pass it and a 450 range blink is not going to help much to escape when you were just on top of someone's face with their team around them. This weakness is even more pronounced by the fact that kassadin can rarely 100-0 his targets until late game (or never really if they get banshees) or if the adc is further from bushes, walls, fog etc they have much more reaction time and you may even need 2 rift walks to gap close which is way too unnecessary when other assassins or like zed, shaco or akali can flank, deal much more threatening burst with longer range gap closers and/or stealth.
Another problem is that you can often no longer rift walk diagonally, as i mentioned you need to by right next to a wall in order to pass it so your possible positioning is severely limited and often out of a threatening range. Your maximum range harass/kill/chase combo is also severely weakened. As kassadin it's often useful when chasing to linger outside of your opponents range while chasing them and then ulting in when your cooldowns are available to go back in. Basically in all instances, your ability to position to assassinate and combo champions is completely crippled and while 450 range is nice for an adc to gain distance from a bruiser it is just too low for an assassin to instantly get onto of an opponent and attempt to kill them especially when that damage is far weaker then the competition of other assassins (fizz, leblanc, zed, etc).
Basically kassadin can no longer position the same as before and positioning is very important to winning this game. Walls, jungle skirmishes in fog and chasing were kassadins greatest strengths and now kassadins ability to position in these situations to ambush and kite has been gutted. People who say kassadin has no counter play have no idea how powerful a banshees is against his damage and how a warded map can prevent his roam. Many champions are excellent picks into kassadin and if you decide to start with a flask alongside him there is no way in hell his 70+25 damage/lvl Q every 9 seconds is going to be an overwhelming harass which leads him to killing you. Even if you do manage to kill someone like lux, there is no way you will be escaping an adc like jinx who will continue shooting you in the face even after you ult away due to the low range.
Even a fed kassadin is quite mediocre now, many champions like a fed irelia, nasus or vayne could already outcarry a fed kassadin quite easily unless kass reaches full build where he is one of the strongest late game champions but now he is a complete joke and deserves the title worst assassin in the game. Lowest burst, low cc, mediocre laning, massive cost and low range on blink ability/gap closer, no stealth, poor wave clear, cant jungle or duo lane at all, extremely low base damage that requires massive farm and kills to scale and has his utility (chasing,escaping,silence,aoe slow) completely gutted. A kassadin who doesn't snowball hard is going to be a complete liability for his team and even while snowballed is not even on the same level as the old kassadin with little to no farm and 1 early drive by kill.