In a sense, every champion in every single match is feast or famine to a certain extent. Every champion (depending on how they are played) has the opportunity to do really well, really badly, or somewhere in between. It isn't a question of FoF or not FoF, it is a question of how FoF a champion is. Having that tension between being able to get going really hard and also be shut down to being useless is a really strong point of tension that helps improve the overall game experience (otherwise you might as well just play a game on your calculator and see who can add numbers together better, because that is essentially what it would be without that tension), and balance of the game is basically built around controlling how much a champion feasts, how much they famine, and what points in the game they do either.
For example, many players didn't like Zed for a really long time because it felt like he was always feasting and never famished, so they nerfed his R last patch, now he has a higher likely-hood of becoming a famine champion any given match. Someone like Poppy on the other hand has a very extreme feast or famine pattern, and some players (like myself) find that incredibly rewarding. However, it is also so binary that it is unhealthy for the game (because when Poppy gets going she really gets going) meaning they have to keep her nerfed quite hard so that she isn't constantly OP.
TL;DR: FoF is an aspect of every champion's kit, and game balance is basically tweaking how FoF a champion is any given match.