Kassadin has been around since the release of the original 40, and has been a problematic character to balance a kit around. His innate mobility in addition to his bursty playtstyle makes him a frustrating lane opponent, and even more so during later stages of the game. But if we look at his damage rotation:
180 (0.7AP) + 20 (0.1AP) + 140 (0.6AP) + 180 (0.7AP)
That's pitiful. He only just topples 500 base damage. LeBlanc has over 800 damage in her QWE, Ahri has just over 750. The problem lies in his mobility. What's been enforced multiple times before is his usage: he should use it aggressively or be punished for not doing so. What happens now is that his first few casts are relatively low cost (there's literally no punishment for his first 3 casts in comparison to his old mana cost and stacking), but he cannot keep jumping after the fourth because 1200 mana is just an insane amount of mana to pay for any ability.
Additionally, nerfing the base damage on his Q is going to make his mediocre laning phase even worse. He was dropped from 280 to 220, then to 180, then E received the same treatment, and for some reason, this calls for another base damage nerf? I'm not seeing the problem. Change his ultimate to something that enforces aggressive use, but limits mobility use, and Kassadin's in a fine spot as-is. Stop touching his already pitiful damage output.
Suggestion: Riftwalk, 20s cd, 100 mana. If Kassadin doesn't hit an enemy champion with Riftwalk, he gains a stack of Riftwalk that doubles the base cost of his next Riftwalk for each stack (up to 800 mana). If Kassadin hits an enemy champion with Riftwalk, the cooldown is halved and he loses a stack of Riftwalk.