Essentially in the easiest to understand way possible Riot wants to nerf and buff champions so that when they nerf champions they just make the weaknesses a champion already has more apparent, and when buffing a champion they want to focus on buffing their strengths to let them shine in the best way possible instead of buffing their weak points and nerfing strong points.
A method like this allows for champions to remain playable even after they've been nerfed, and remain balanced when buffed.
Riot has recently taken this policy to avoid things like when they nerfed Evelynn into the ground and made her so bad that players were getting banned for picking her in ranked for aiding the enemy team (this actually happened)
When a champion has no clear weaknesses, or when buffing their strengths would just result in a toxic champion and nerfing their strengths would just make them too weak to play they need to think about reworking that champion. That's why champions like Taric, Sion, Karma, etc. have seen reworks over the years.
This is why Morello has basically stated "sorry Poppy mains, but if your champion becomes popular expect one of two things to happen: Poppy getting a rework, or Poppy getting nerfed into oblivion like Evelynn was" She has a toxic kit, and needs a rework, this is why things that "upset the playerbase of a certain champion" need to happen. Because *** those people they don't really matter, learn to play a new champion you piece of ***.
What exactly were Fizz's, Akali's, Zed's, and Ahri's weaknesses and Strengths?
As far as I can tell their strengths were generally somewhere along the lines of:
Can split push because they can 100-0 anyone who tries to fight them
Can single target burst and 100-0 someone
Extremely mobile to get in and out without risk
With weaknesses along the lines of:
Can't do AoE burst I guess?
Idk they can't build tanky and do lots of damage probably?
Uh they can't assassinate the player so they aren't really infinitely powerful I guess
In a case like this pseudo-reworks(the entire champion isn't being picked up torn apart and remade they are just getting number tweaks, minor skill updates, and if you want to call removing an item a champion rework sure why the *** not) they aren't really reworking a champion to make them different due to archaic mechanics that just don't really work anymore as the game grew, but are instead giving champions that don't really have weaknesses some sort of weakness, even though it really isn't
I suppose they could have made Zed, Ahri, Fizz, and Akali AoE burst less, but that wouldn't make sense because it's pretty much already non-existent.
Instead what they have to do is say "Well let's give these champions a window of opportunity, if they land the skill shot they can burst someone, if not then *** it they need to try again later"
In the case for Akali it was more of a "Haha *** you Akali mains" and in the case for Zed it was along the lines of "Haha, yeah we 'nerfed' Zed"