Yeah, kill systems are fine if it's based around an rpg type game, or if the story doesn't take itself too seriously (looking at you "I've been killing slimes for 300 years and maxed out my level"). In a fantasy setting that isn't based on a game though, I'd prefer a system where exerting oneself beyond their normal limits would raise a stat, and once the total of all stats reach a certain threshold the character levels up. In a system like that it'd be easier to justify characters having class archetypes or fighting styles beyond being born with a talent for a class, or having innate magic talent.
Maybe you could have increased stat gains during a fight to show exertion, and also because it's dangerous; for instance maybe evading attacks, or trying to escape might increase agility or stamina, while successfully blocking attacks might increase defense or constitution. And for training you could have reduced stat gains since it's safer, and more of a grind. Though the only flaw for that type of system that I can think of would be the difference in experience between someone who's battle hardened by facing off against difficult opponents with varied strategies, and someone who's only ever swung a sword at a training dummy and ran until they were exhausted in the safety of their training area. And while I say that's a flaw, I think it'd be neat to see a story, or even a story arc based around it.
I suppose if someone were dead set on doing a kill system though, they could probably change the experience gain based on what took place in the fight. For instance, a character could kill a monster significantly weaker than themselves and get reduced or even no experience points; or increased experience points if they kill a significantly stronger monster, or kill it by targeting weak points. I dunno, it could be my own bias, but I feel like using a variety of fight choreography and different numbers breaks up the monotony of "kill thing and get 10 exp, kill 10 things and get 100 exp"