Like for example x item gives you super fast attack speed but your crits do alot less damage. that is just an example and im sure these items would have VERY specific stats so they arnt used on certain champions and never picked up on others.
What I mean by that is for example an ADC who doesn't use a lot of crit in their build could just buy that with no trade off.
TehNACHO3 votesThere used to be an item that had an active that gave you 200% attack speed and guaranteed crits for 3 strikes, but you lose the item's given attack speed(?) While it was on cool down.
So yes. It was underutilized and otherwise hyper niche, so it was scrapped.
ProtestantCaesar2 votesSword of the Divine. It was pretty cool.
Meep Man1 votesGood god, it was cool but did it break a few champions when they were popular. Build one actually decently cheap item and then get the best burst in the game for 3 attacks. Building it on Rengar, Vayne, Twitch, Draven, and Talon honestly felt disgusting.
Flaherty2 votesKnight's vow is kind of like that, reduce damage for a teammate but take more yourself
Asayake 5150glow1 votesKnight's vow is kind of like that, reduce damage for a teammate but take more yourself
Not really, you get extra defensives while near your teammate don't you?
Flaherty1 votesYou get 40 armor but 12% of the damage your partner gets is directed towards you as true damage
Asayake 5150glow1 votesYou get 40 armor but 12% of the damage your partner gets is directed towards you as true damage
So you're taking the exact amount of damage which your ally would've taken (hence true damage, since I'm assuming the amount you take is calculated after their resists).
Makes sense.
Mysticman892 votesSo, you're suggesting items that have explicitly negative effects, instead of just the 'cost' of using up a slot that could be used for another item?
I don't know how much thought they've given to any items of that sort, but if they did, they'd have to be super careful to make sure it was actually a negative no matter who bought it, otherwise it'd quickly become a must-buy on the ones who didn't care about the trade off.
Mejais is probably the closest thing that exists since with a couple back to back deaths you can quickly have an almost useless item on your hands, but with the breadth of champs in the game it's hard to make risk-reward items that are balanced on everyone.
Slythion2 votesthat's exactly how you get abuse cases.
champion that can use this items while the drawback doesn't effect them would be incredibly overpowered. For instance, any on-hit champion that doesn't crit would be broken from your example.
xxbrad2o12xx1 votesThat's exactly why I said stats would have to be thought out to prevent something like that. I am sure there is something out there they could do in that regard but yea what I was using attack speed minus crit as an example so people knew exactly what I meant.
Slythion1 votesidk how they could play around with the stats. The simple fact is that some champions would be able to use items like this with absolutely no downside makes a balance nightmare.
Either the advantage stats are sub-par to ensure that one group of champions don't have access to superior items that everyone else doesn't. this would result in a "why would I build this item when it's stats are the same as all the rest" case for the unaffected champions.
or
The items would have better stats and then the unaffected group of champions would have access to free better items while the rest were stuck with the regular stat items.
There's no way around these situations without a "well maybe if we adjust the numbers just so then it might not break too many champions but next patch will change the power distribution and we'd have to re balance it all over again"
I'm not trying to be rude, just trying to explain why it wouldn't be possible
Titanium701 votesI really hope we'll get some of these one day. While it could be a problem on carry roles - Tanks and Supports (non-carry/snowball roles in general) could get amazing itemisation options unabuseable by other roles.
Something like: Restore 25% of incoming DMG -> DMG dealt by your abilities and autoattacks is reduced by 50%. 1000HP 40 Armor. 3000 Gold. A heavy lategame Item exclusively for tanks with synergie in Spirit and Thornmail, counterable by GW. Fair enough?
Honorable mention: 
ChaddyFantome1 votestechnically, 
line already is one since the passive on hit effect disables if you kill a minion.
Bellows1 votesSword of the Occult was one of these and so is Mejais.
In a way that is....
I think something like that could be nichely abused by the pros too hard.
I am sure riot has thought of these items but items like that could easily have an item that counteracts those tradeoffs as well as runes and masteries that could counteract them. They just are not that viable. (Also what adc doesnt use crit in their build?)
Mysticman892 votesCorki sometimes doesn't opt for crit, and before crit vayne was a thing she didn't build much crit. Plus there was a whole swarm of adcs who just built armour pen instead of crit before the lethality changes, so there might still be people who opt into a lethality build on adcs although it's not nearly as good as before.
xxbrad2o12xx1 votesJust an example I used and @Mysticman89 explained it pretty well.
Magimodeller1 votesI am sure riot has thought of these items but items like that could easily have an item that counteracts those tradeoffs as well as runes and masteries that could counteract them. They just are not that viable. (Also what adc doesnt use crit in their build?)
On hit builds. Kog used to with his 5 AA/s, don't know if he still does, Kalista is only 'viable' with on hit since she only gains 90% of any bonus AD, Twitch jg also used this season, Muramana Varus, Muramana Ezreal and Muramana Urgod. Not the best type of build right now so most who build are out of the meta or have better builds. Edit: Oh and Vayne used to build on hit too when she wasn't meta