Cool. I actually somewhat agree with you about the flavor and immersion benefits, but I ultimately don't think it's worth the extra burden of knowledge things like this would add. To me, this is one of those "great in a vacuum, but not so great in practice" kinds of things. Here's why (again, only my personal view):
Being able to say "hey, Lux counters Zed because light banishes shadows" is really cool. But no matter what, we're also going to have the "hey, Urgot counters Zed because he can suppress the all-in" case. So adding these thematic interactions is just adding them ON TOP OF existing mechanical interactions.
What worries me about that is that we'd add a bunch of one-off interactions, with the ultimate result being that we just shift around which champs match up well against each other. And in exchange, determining these matchup strengths now relies on mechanical AND thematic understanding.
It's extra complexity, which isn't always worth it. Right now we might have a "rule" that Zed beats poke mages. But with the added complexity, we have that Zed beats poke mages, unless they use light magic. Then you add in skins (does Arclight Vel'Koz counter Zed too?), and suddenly it's a major can of worms.
Where I think these things can be really cool is when you have a game that relies more on strategy than mechanical play. Card games, puzzle games, even some adventure games - you can really start to leverage these better, because those games are less focused on "this gameplay pattern is strong against that other one". That means you aren't doubling up on the complexity.
Pokemon comes to mind as an example of this. You make a TON of pre-game decisions (which Pokemon are on my team, what moves do they have, who leads, etc.), but once you're in the game, your options are pretty finite. This lets the game challenge you to work around thematic interactions, because you don't have to worry too much about broad strategy (you did that part already).
But because League of Legends has so many instances of strategic AND split-second decision-making DURING the game, adding in an entire extra set of thematic interactions is probably too much of a burden.
Interactions like the Rengar/Kha'Zix one are less of a concern to me, because they're more one-off and strategic in nature. I wouldn't mind seeing more of them, personally. But, as you noted, they're also less impactful, and probably not the reason you would pick either champion. It's also hard because you'd need both champs to be in favor at the time; maybe if there were more of them, we'd see teams making choices based on it?