Kassadin actually has really low AP ratios for his burst combo: 1.9 (+ 0.15 per W AA, but that isn't really burst anymore), so just stacking pure AP on him doesn't work as well. LeBlanc's full combo, for example, has a 3.76 AP ratio. LichBane improves his use of AP significantly (roughy 50% increased AP ratio if all you do is RQEW attack, which can easily be improved on), and mana is important so that you can stack his ult, so rushing a Deathcap on him like I see a lot of people do isn't a great idea. Waiting until after LichBane to build your Deathcap makes it much more valuable.
I'll also agree that Ahri is best played as a poker, rather than an assassin. Fizz is kind of tanky dps, although with more bursty damage than most in that category. AP Shaco is good against a team that doesn't know how to deal with him, but isn't that great most of the time. Kass is banned almost all the time, so you can't depend on him.