Im really not seeing Kassadins damage, yet riot referred to him as a late game monster

This is taking into account all of the games that I've played with him since season 4 (omg so far back nr). But Ive never done much damage as him and im including games where I've been 27/x/x or such. I love the whole anti mage playstlye that he has, But he's "feels like" he has less burst than say, Ekko (who was described upon release that his playstyle was to wittle his enemies down which he does do, but none the less I can see the burst difference between an early 4/0 Ekko and what i just was until realizing just how much gold the enemy Caitlyn, Chogath being chogath, etc as a 4/0 - 4/x Kassadin. Is he just not a bursty assassin? Or does he need a buff of some sort? He feels fair in lane both playing as and fighting against ( playing as Kat vs Kass, however, is the most powerless I've ever felt) But his snowballing just feels really weak in comparison to the other assassins. Even galio another anti mage type champion (completely differnt playstyle though admittedly) snowballs alot better it seems. I dont know is it just me or is Kassadin actually just as strong as the other champions in his "category" and I'm just underestimating him? I must admit his mobility lategame is amazing, but even with that, the lack of actually burst damage which i would expect from an assassin in general makes me feel otherwise.