Looking into the past media that has this type of character, the "unfeeling person who went through some stuff but is back to relativly normal activities"... this type of character hasn't been well received when in an action-genre of story.
Take a look at "Atomic Blonde".
The movie is based on the same archetype that Kai'Sa is, however the movie doesn't do the right thing to expand properly on this type of character, to ground the character in some sort of reality and allow the audience to see and feel with the character.
The types of movies that do well with this archetype are moveis like "Gran Torino" in which the entire story is about building up from nothing. The change is gradual and the way that the movie's message gets to the audience comes at the final scene where a climax is reached to a problem(not spoiling that amazing movie). "Gran Torino" has a message of "stopping puts you down, so get up!"
In league, that would be insanely hard to pull off. I don't blame Riot's writing team for messing up this archetype because of how the archetype simply doesn't work with the action-genre.
"Atomic Blonde" didn't have any emotional connection that grounded her to the audience.
Kai'Sa is lacking in this emotional connection within her story, and THAT is what is throwing her story down the "Atomic Blond" trap.
An attempt to make Kai'Sa "cool" and "rugged" has instead resulted in a shallow character whose entire existence can be summed up in a 18 word sentence with little/nothing else that's possible to add onto her story.
"She was lost from her daddy in a scary world, forgot about her past life and became deadly"
If Kai'Sa had managed to MEET her father, Kassadin, then this in turn would change the dynamic of her arc to make a more complete story. It'd be a reconnection story between Daughter, Father, and Void creatures who want to separate them.
That alone has a good 50-pages worth of story possible.
Maybe Kassadin was fighting Malzahar but then Malz managed to open a portal into the Void and unknowingly unleashed Kai'Sa into the limelight.
Kai'Sa would proceed to not know who Kassadin was, would beat Malz up because he would be caught off guard, and then leave the general area where the portal she came out of was. Kassadin could attempt to follow her and see if She was his daughter.
That alone creates the ability to write 30-ish pages worth of story(possible 2 seasons of a TV show if you threw in 2-3 filler episodes).
Riot could have taken a lot more creative paths on the story, unfortunately Riot fell into the same trap that "Atomic Blonde" did and proceeded to have a newly released character become bland.
's lore (besides the daughter part). Plus I like how nice she is to her supports compare to Xayah whenever she's not with a Rakan support.