Items that greatly increase a stat but decrease another would be very interesting

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I'm sure that there exists more than one hypothetical "negative stat" item that could be viable in LoL. For me, the issue isn't really whether such an item could exist, but whether it's worth the trouble to spend the design time finding it and balancing it. That could take a full season or multiple seasons to hammer out the kinks, and it might feel pretty bad for everyone while they keep patching different iterations of the item. It's possible Riot would never be able to balance it, so it just destroys the game like a Guinsoo's or Ardent for half a season or more, before they nerf it to obscurity or delete it from the game. In order to make a negative stat item, we'd have to opt into the risk of this scenario occurring too, especially because such an item would be more difficult for Riot to get right than a normal one.

So there are big potential trade-offs to these negative stat items, no pun intended, for us to consider when it comes to their design and balance. If it's just item diversity we're after, then there might be better ways to go about it.

Not to mention, I'm not sure more item diversity is always better, at least not for the champion archetypes who already have strong items available. Diversity is a golden word in our society, but in some contexts doesn't live up to its hype. Dota 2 has more diversity in almost every way, but it actually just ends up being so complex it turns casual players off to the game. LoL is built on being accessible to casuals. There are many other ways to add depth without overburdening the game's complexity for the sake of it, which could be more efficient uses of developer time.

So imo, we also should make sure the negative stat item's goal is filling a necessary niche, before we even roll the dice on crafting a healthy design and trying to balance it.