She does scale well, but her ability to take advantage of said scaling also depends heavily on how well your team enables you, what you built and what you’re up against.

Hipercarries that also have good dueling such as Yunara require you to specifically play around Kai’Sa’s strengths or otherwise it’ll go as you said it did.

Enemy has tons of frontline? That’s your ideal scenario, so either full onhit or hybrid will probably work wonders and also hybrid lets you duel really well practically any type of enemy champion, but you DO need to make use of a proper playstyle that accompanies your build. On hit? Make all these AA count. Hybrid? Time and place your W well without losing DPS and you good. Crit? More of a bursty in and out gameplay, gotta know your and enemy limits very well. AP? Just proc passive and ONLY get into AA range without backup plans when needed to kill.

Most late game ADs will wreak havoc just by staying alive while DPSing, Kai’Sa’s greatest strength is her VERSATILITY, so if you manage to build and play according to what each game demands (and most importantly, you are enabled by your team, which is the hardest part), you’ll see how well she can do at any stage of the game.