Kassadin's biggest problem is that he cannot be an assassin while having the amount of mobility currently in his kit. If he is balanced around being able to assassinate a target, then he is far too safe and gating him with mana and weak laning is never going to be enough to counteract that until forcing him into non-viability. They need to push him into the role of an anti-mage skirmishing DPS champ.
To do this they need to:
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Lower his burst across the board (in some places pretty substantially)
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Lower his cooldowns (in the case of his E, remove the base cooldown and run off of the spell charges only)
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Increase his durability (both through his passive magic resistance and the strength/duration/uptime of his shield)
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Lower his mana costs (especially his ultimate, because once they fix his gameplay he won't need to be shackled by mana as severely)
If they do this, he'll be more focused around popping into fights, landing a few spells, jumping out, and overall being a slippery DPS champ. He won't be able to insta-kill anyone, but he'll be more effective overall while being healthier for the game and easier to balance.