You're the worst.
So, before anything else, I'd like to point out King's Rock gives a 10% flinch chance, not 20%. So, with Skill Link, multi-hit attacks have ~41% chance to flinch, not these straight absurd numbers people have been putting out here.
That applies to pretty much every hax item; Incense + Brightpowder are 10%, Focus Band is 10%. The only one that isn't is Quick Claw, at an incredible 20% (wowee OPOP xD).
So, before continuing on, I'll acknowledge what has been said before; The only reason these items are still banned is because of a combination of several very specific reasons.
They have been banned since waaaaay back when they were introduced, because some random staff member stuck it on the clause list back in 20whofuckingcares.
They're annoying, and them being unbanned doesn't really add anything of competitive substance to the game, so nobody has cared enough to pursue their unbanning in any meaningful capacity.
Even in formats where hax items are legal, they're basically never used. As a result, most people have either never actually seen them used, OR gotten haxed by them at 1077 ELO on the Showdown Ladder one time and hate them. (Ignoring all the times they probably ran into someone using them, but didn't know, because they didn't proc); As a result, most people don't actually know that much about them or how bad/good they are, just that they're an RNG mess.
With that being said, what I 100% disagree with and will dispute, is the idea that these items are in any way banworthy. In fact, I'd argue that if the question wasn't "Should they be unbanned?", but rather, "Should they be banned?", it would be taken about as seriously as suggesting Sand Attack or Dynamicpunch should be banned, because these items are actually fucking awful.
So, with that in mind, I'll go down the hax items in order of (what I believe) are the worst, to the ones that might actually have some use. None of them are even remotely banworthy as far as I'm concerned, but there are some that are just obviously inferior.
Additionally, I'm going to state something that should be obvious, but is basically always ignored in this discussion for some reason; Losing your item slot for one of these items is insanely bad. Sure, lowering enemy attack's accuracy by 10%? That sounds sweet. But then you remember how incredibly important and useful items are in Pokemon, and you realize that giving up an item slot for an item that, the majority of the time, in a majority of games, is effectively worse than nothing (because at least doing nothing doesn't lose a slot over a better item), and the items start to look a lot worse.
1: Focus Band
Effect: If a pokemon holding a Focus Band is hit by a damaging move that would cause it to faint, there is a 10% chance Focus Band will activate, causing it's holder to survive with 1 HP.
So, first of all, Focus Band. Before even going into anything, I'm going to outright state that in 99% of scenarios, Focus Band is significantly worse than Brightpowder. Brightpowder lowers the accuracy of all moves attempting to hit you by 10%, whereas Focus Band will only ever activate on moves that are KOing you at the same % chance, leaves you at 1 HP, still leaves you vulnerable to literally everything other than direct damage that would KO you, still leaves you vulnerable to any chip at 1 HP, etc.
So, aside from being generally worse than Brightpowder, Focus Band is just awful. Full stop. A 10% chance is pretty awful. A 10% chance to save you when you would die is really bad, because it effectively means that for it to be useful, you have to knowingly send your pokemon to it's death, praying that a 10% chance will proc and give you an extra turn. And for all that trouble, you're still left at 1 HP, vulnerable to sandstorm, hazards, status, sneezing, a breeze in the wrong direction, etc.; A majority of the time, a Focus Band does effectively nothing, and even when it DOES do something, your pokemon is far from "unkillable"; Even in the worst case scenario where your opponent's Focus Band activates and they KO your pokemon, it should still be trivial to revenge kill. And while you might think that a 10% chance to survive is better than nothing, in the same way you might desperately fish for an Ice Beam freeze when you're about to lose, the difference between this and Ice Beam is that Ice Beam is good independent of a 10% freeze chance; Focus Band actively makes your pokemon worse by holding it.
2: Quick Claw
Effect: A pokemon holding Quick Claw has a 20% chance of going first in its priority bracket.
This might be surprising to see second, because unlike the other hax items, Quick Claw actually has a decent activation chance; 20% is a lot better than 10%, and that can't be ignored.
With that being said, Quick Claw suffers from the same problem as Focus Band, in that it CAN get you some free hits or even a KO by activating when your opponent doesn't expect it, this does mean that a lot of the time, you're putting yourself in a terrible position and banking on a 20% chance to turn it favorable for you. What ends up happening instead is that, a majority of the time, you'll lose the gamble and be down a pokemon.
Ultimately, Quick Claw's effect of going first is something you want to happen reliably in order to properly abuse it (ie, slap it on a really slow, strong sweeper), but it's low % chance of activating means that trying to rely on it frequently results in it failing and your pokemon being KO'd, or it activating on turns where going first doesn't influence the game at all. Not only that, but going first doesn't necessarily help you against defensive answers a lot of the time, and Quick Claw doesn't ignore priority, so that remains a viable option to deal with any potential Quick Claw threats.
It's an inconsistent effect that wants consistency in order to be abused, and because of that, it's just garbage that eats up an item slot that MIGHT win a game every now and then, but loses much more games because of the item you lost to use it.
3: Brightpowder/Lax Incense
Effect: A pokemon holding DumbItemName reduces the accuracy of moves targetting them by 10%.
So, to begin with, let me clarify the effect; It doesn't subtract 10% of the attacking move's accuracy, but rather it decreases the incoming move's accuracy by 10%. So Flamethrower would have 90% accuracy, whereas Zap Cannon would have 45%.
Bright Powder is up here because it's effect is actually decent; Unlike the other 2 items, you don't have to put yourself in shitty positions for it's effect to matter. A passive 10% accuracy decrease, while incredibly low, is still usable because it's always active, making it significantly more likely to impact the game than other hax items that are narrowly useful, and encourage putting yourself in bad situations for the roll to matter.
Unfortunately, that's only the case if Bright Powder has no opportunity cost. However, because there is an opportunity cost, (loss of an item), Bright Powder just isn't worth using unless there's literally no other item that would be better for you to run (aka I doubt it, kiddo).
Of course, this is subjective, but I'll illustrate my point with my favorite thing to follow: Precedent.
The best comparison between the 10% Evasion items is the Sand Veil bans in gens 4/5, an ability that increases Evasion by 20% while in Sandstorm. Unlike the evasion items, Sand Veil had basically no opportunity cost for it's main abusers; In gen 4, all Gliscor had to give up was Hyper Cutter, effectively only useful for Intimidate, in exchange for an effectively always on 20% evasion boost. Similarly, in gen 5, all Garchomp had to give up was Rough Skin for a passive 20% evasion boost, letting it abuse some ridiculously stupid sets, like Sub-SD, fishing for a miss and then boosting up. The ability had effectively no opportunity cost to use, since Sandstorm being up in Gen 4 is incredibly common between TTar and Hippo and no real competing weathers (lolAbomasnow). Gen 5 had weather wars, but again, Tyranitar alone dwarfed the other starters in usage, not even accounting for Hippo.
So, naturally, this brings up the discussion of how much better Sand Veil is than Brightpowder. Sure, it's a difference of 20% and 10%, and a useful item slot vs a significantly less impactful ability, but how much does that influence the actual utility of them as evasion-boosting nonsense? Well, the most obvious comparison would be comparing the previously mentioned Sub-SD Chomp set vs a hypothetical Sub-Setup Brightpowder user.
First of all, I'm going to assume 5 Subs for the Garchomp, assuming Leftovers and enough HP to be able to setup Sub 5 times, but I'll throw in 4 sub chances too, in case you're scared of massive Spike setups or something. The Brightpowder mon will get 3 Subs, because their lack of lefties means it's incredibly likely they'll be chipped somehow (Weather/Hazards). With that in mind, here's the chance for each prospective set to get a Substitute up while the opponent misses:
5 Sub Chomp: 67.2% Chance
4 Sub Chomp: 59.0% Chance
3 Sub Bright: 27.1% Chance
4 Sub Bright: 34.4% Chance
In case it isn't obvious, this is a massive difference. Yeah yeah sure you could run Brightpowder on anything, instead of Sand Veil being on just a top-tier OU pokemon, but the difference between Sand Veil and Brightpowder in these instances is that one has a significantly larger opportunity cost. Ultimately, this is one of the better hax items, in that it could potentially see some use, unlike the other two just being meme-tier, but I hardly think it's any more problematic than currently legal RNG-exploiting moves/abilities/strats/fucking whatever dude.
4: King's Rock
Effect: A pokemon holding King's Rock has a 10% chance to flinch on any attacking move that does not already have a Flinch chance.
This is only up here because Skill Link King's Rock is actually kind of a real thing. Any other application of King's Rock is pretty much Focus Band tier to me, so it's not even worth mentioning; If you understood what I was getting at with Focus Band/Quick Claw being bad, you'll probably get why 10% Flinch is similarly not excellent.
So, with that being said, let's talk about ~41% flinch chance, and why I don't think it's anywhere near as scary as it might seem. (Although it is a little scary)
The most important thing to understand is that King's Rock Cloyster is run in lieu of another, more consistently relevant item; White Herb to minimize damage taken and make you less susceptible to priority attacks, Life Orb to hit harder and nab some more KOs, but making yourself more susceptible to getting whacked by priority, Focus Sash for a really reliable setup along with good hazard control as a reliable, scary lategame sweeper, etc.
Every potential item has a use, and which item you choose depends on how exactly you want Cloyster to slot in on your team. In the case of King's Rock, although it does have a scary flinch chance, I think it similarly has a specific niche. It's an item that gives you a chance against defensive, bulky answers that hope to KO you after tanking a hit, that LO isn't enough to push through. It isn't necessarily objectively better than other item options, and even with a decently high 41% chance, is still unreliable against anything that can take a hit and then threaten to OHKO you, but can get the job done.
Does getting flinched by it suck? Sure, maybe. But it's not exactly a gimme; It's 1 item on 1 pokemon that, although useful, is in the place of other, more reliable items. Ultimately, the best answer to Cloyster (and really, every shell smasher) is and always has been to not let it set up, not deal with it afterwards. Ultimately, King's Rock lets it snatch victory from the jaws of defeat some of the time after it's setup, but it doesn't help it get there, and it doesn't always work. It's certainly not quite as obnoxious as other RNG bullshit, like pretty much any Serene Grace user.
Anyway, that about covers everything. Hax items are too inconsistent to be significantly abused, and come at too great a cost to just slap onto things and hope it wins you a game. Using them loses you a lot more games than it wins you, and while getting R1 Haxed by Quick Claw feels shitty, people aren't going to win tournaments off of the back of these things, and if someone somehow does, I don't think that's any more likely than someone winning a tourney off the back of crazy crits and bad misses from the opponent.
Ultimately, my biggest gripe on the matter is that hax items aren't even that bad. Compared to other RNG strategies like anything involving Serene Grace, they have a higher cost to abuse, are less likely to influence the game, and a lot of the time, aren't even as high-impact. The reason hax items are banned isn't because they're strong or overwhelming, it's because losing because of one, even if it's incredibly unlikely, feels awful. Because 99% of the time, anyone using these items is probably bad, to the point where they don't understand why these items are bad, or what's bad about them, so people would prefer not dealing with them. But I don't think that's exclusive to these items, and they're certainly nowhere near the top of the viability hierarchy on such strategies.