Why champs are considered infuriating (just going for the name drops):
Zed
Pros: Easy wave clear, Bonus %AD, practically resourceless (Energy costs are not meaningful), High mobility, situationally untargetable, long range spamable poke.
Cons: Ult telegraphed, builds glass cannon, melee.
Zed's risk exists only in team fights. He's a top teir duelist at all levels, lane bully early game, and split pusher mid/late game. He's useless when shut down, but is exceedingly hard to do so for most of the champion roster. The risk/reward paradigm just isn't there.
Riven
Oh gods, the snowball potential. High mobility, high burst, high DPS, AD scaling shield. Thankfully they nerfed her early game.
The real problem with Riven is the burst. I've never had problems with your standard riven; but you can always recognize a regular by the animation canceling. She can turn what should be about 3-5 seconds of DPS into a Rengar Style insta-gib - Starting with a Stun!.
Of course, only Riven and ADCs (orb-walking) are allowed to animation cancel. Do it on anyone else, and it's actually bannable!
Lee Sin
This guy is actually easy to summarize: "kit overload".
High mobility, high base damage, high scaling, good sustain, High utility, blatant favoritism by Riot. The only thing keeping this guy in check is his skill floor.
He's [debatabley] the flashiest champion in league and one of the most consistent picks in pro play. He's so strong, that he has single-handedly dictated the jungle meta for most of his existence. And the moment he falls out of favor, the bastard gets straight buffs quality of life improvements that shouldn't affect high level play.
Because of this, he's also one of the most popular champions in league. And lets be honest, playing him properly is hard. Which means riot can just rattle off his win rate at low elo and claim he's balanced (For any other champion, "win rate is rarely indicative of balance").
But I digress. Lee Is just flat overloaded. He has all the tools to out-play most of the champion roster when and how he wants with incredibly safety. You don't actually beat a good Lee, you're just there when he F's up. Unless you play a specific subset of OP champions, allowed to exists for the sake of jungle diversity (see: Lee, Elise, Vi jungle of S3).
Fizz
This guy is also easy.
High burst and mobility is fine on an assassin - they're basic tools of the trade.
0.75 seconds of untargetability every 4.4 seconds (45% CDR) attached to a 400 range dash. . . Now we have an issue.
Troll pole your initiation, combo you, troll pole your retaliation, turret dive for the kill, troll pole turret agro. "outplayed"
Give the troll pole a more meaningful CD, and he won't be an issue.
Yasuo
Admittedly, I don't have the most popular opinion on this one. I'm all for the out-play potential on this guy. I'm not all for the ridiculous amount of safety nets he gets.
I've trashed him with hard counters, hard countered, and just about everything in between. And for all my hard work, what do I get? He can't solo carry the game anymore. (>_>)
Weaknesses/safety nets:
-Situational ult
But can be used on any displacement; not just knock-ups and not just his own.
-Situational mobility
But has almost no CD and is strongest in lane phase.
-Situational CC
Requires 3 Q stacks, which last 10 seconds, has no resource investment, and super low CD.
-Reduced late-game DPS
In exchange for a lot of free stats resulting in super early power spikes ensuring that he never truly falls behind meaningfully.
-squishy
Has a huge low CD shield refreshed by ult and windwall.
-Windwall has a high cooldown
It completely deletes any bullet that touches it (and associated skill) resulting in some weird interactions (see Nami and talon ults). Has a hit-box bigger than him, which means he can sit in for 4 seconds of 100% projectile immunity.
-often gets focused in teamfights resulting in above average death counts
Gee..... I wonder why?
Point is: Yasuo either hard carries, or is average. Beating him means nothing, losing means you potentially threw the game. That is infuriating.
LeBlanc
Dash->blink back, repeat.
Slow->root, repeat.
Burst 1/3 your health, repeat.
Ya, her ult makes for some really f'ed up combos.
Oh, look, you caught her!
. . . Oh look, it's her passive again.
There's a reason a lot of junglers don't bother ganking LB.
Irelia
Punishes you for punishing her. Passive is super annoying in team fights.
Vladimir
A tank that heals and does damage - both in spades. Troll pool.
Enough said.
The common trend with frustrating champions isn't when they are OP/UP or they're ability to play around others. Give them every tool in they world, I don't care (personally). The problem is when those out-play tools remove or severely limit your ability to out-play them in return. When your only option to beat (not just go even) another champion, is to hope they F up, there's a problem. Similarly, you have a problem when beating a champion has no significant value.
I don't mind getting out-played. I welcome it. Just like you said, losing in a match of skill is interesting and potentially educational. I got trashed by a Nami mid once - one of the most fun lanes I've had. I've done Vel'koz/Zyra and Veiger/Azir match-ups - had a blast. But I had equal control in those match-ups; I wasn't dependent on my opponent messing up before I could do anything.
EDIT:
{quoted}
its also infuriating to have champions that have 0 outplay potential because they are outdated and poor champion design.
people know what lee sin does. what yasuo does. what fizz does. etc to outplay you. you just can't do anything about it. i wouldn't consider it outplay if i cant do anything about it. other than not fight at all.
This is also something to consider. Some older champions don't really have the tools to deal with some of the newer designs. I'd consider this more of a supportive factor than core; but I can see it coming into play.