All of the champions mentioned in the OP have mostly back-loaded burst. Kassadin, by contrast, can initiate with all of his damage, even if his E charges up slowly outside of big fights. Kass's fantasy, among others, is also having unrestricted mobility, something he doesn't quite have (he's mana-gated), but achieves better than any other champion, even Talon or Quinn.
In the end, Kass will have to choose between being the most mobile champion in the game, and being the best anti-mage. Those are two distinct core identities, and he can't really be both without paying heavy costs. Personally, I think he should choose the former over the latter, even if his kit could still do well against casters.
Beyond that, Kassadin still has gameplay issues that have been left unresolved for years now. He has a ton of instant, upfront burst on top of near-guaranteed initiation via mobility, something that has never turned out healthy in League, with Rengar as an example. On top of that, all of his current anti-mage protection, i.e. his shield and passive, would be much better suited on a bruiser, and can't be made that great on someone who isn't going to be building much health or resists. He needs a bit less reliability on some of his abilities, namely his point-and-click Q and E, and with that a bit less upfront burst, and with that he could afford to have much more assassin-appropriate utility against magic damage and casters.