In effect, yes, avoiding using a physical attack on Kartana against a Zapdos is competitive, and able to be played around. Because in the gran scheme of a game that isn't fucking HO vs HO, where Kartana will be sent out several times, and Zapdos will probably live, it is almost a guaranteed chance that Zapdos will get the paralysis. This makes Static a "RNG" ability, but it is also, at the same time, competitively consistent.
Here is an example from Toxapex. Staying in on 0 Attack Landorus-T and using Scald. Even if this does not burn, this play is not fully fueled by "risking it all on a 30% chance", as the Toxapex player is confident that they will be able to rack up Regenerator healing and be able to do something similar, again. This and other examples especially makes Scald, not in effect about RNG, but actually competitively consistent.
You say that individual Pokemon should be banned for King's Rock, like Cloyster. When would King's Rock finally reach that barrier of "breaking enough Pokemon"? And I'd like to also say this: Cloyster, the Pokemon itself, has competitive value. Being an option on teams even without King's Rock, or in lower tiers. King's Rock, however, does not actually add any value to a tier like Gen 8 OU. It is also not consistent enough, because playing around King's Rock flinch is not something that can be played around from Turn 1. Cloyster cannot generally fish over and over again, making a check like physically defensive Toxapex a "well lol, lmao, get fucked because didn't teambuild!", it is usually down to one single turn for the opponent to make a move, and for most viable teams, needs to just not get flinched.
You could argue that banning Cloyster would get rid of the majority of this. I would mostly agree, but why keep King's Rock? It is an item that is only there to be abused and become an uncompetitive force, what value does it add to any Smogon tier? You may say "well, duh, to buff Cloyster/Maushold/etc.!" But that isn't the only thing that it does, it also enables unsavory playstyles and has potential.
In short, I find your argument to not be sound, from the perspective of: Game design. I feel like people in Smogon forums and the like often do not understand, that at the end of the day,
Smogon 6v6 Singles is not the same game as Pokemon Scarlet/Violet. And Smogon acts as a collective game designer. A game designer that cannot create new elements, but actively makes decisions that changes the game and influences different play. Banning Volcarona was not a decision the council made just because they felt it was uncompetitive, but it was a game design decision, a metagame design decision, believing Volcarona's defensive utility on teams to not be worth the potential trouble for upcoming tournaments.
As a community we must not forget that we hold the keys collectively to the game design of what we want to play, and that choosing to keep things like Quick Claw/King's Rock is not a neutral game design choice, it is biased, with the language of neutrality. You have decided that keeping things for the sake of keeping things is more worthwhile to the game, than patching up potentially uncompetitive- no, objectively uncompetitive elements.
On the topic of "holding an item = competitiveness", no. Things such as picking an ability (Sand Veil) is also not a competitive choice, despite being technically a trade-off. Garchomp is actively better on average with Rough Skin, and choosing Sand Veil instead is not enough to make something competitive, because it is consistency that makes something uncompetitive.
I've heard some float around the idea that items (like Scope Lens) that increase the odds of RNG-related effects from occurring are also in the category of uncompetitive. I absolutely disagree, because I see these as creating more consistent results, rather than the otherwise. For instance, Scope Lens + an ability like Sniper makes Critical Hits an expected result throughout a game, and not something that is expected. I would go as far as to argue that things such as Serene Grace actively make moves such as Flamethrower more competitive. Because I am here to present this conclusion:
Competitiveness and RNG's relationship is about expectation and agency.
It is not simply "the more RNG effects the more bad uncompetitive" that makes something like Quick Claw banworthy to me, it's that it removes agency from the opposing player while something like Serene Grace is not.
Getting flinched by Jirachi Iron Head a few times is not Serene Grace making the game less competitive, because that is actively the expected result of the interaction, and can be played around as a result, and unlike something like Quick Claw, can actively unironically be stopped. For one, a Pokemon like Ferrothorn can literally kill something like Scarf Jirachi for trying a stunt like that. Two, if not Scarf, it can be outsped. Three, what makes Shaymin-Sky banworthy isn't "RNG", it's actually how consistent it is at proc'ing effects that removes the opponent's agency.
Quick Claw being 20% and having such a drastic effect means that there is no real way to actively combat it, while also not being consistent enough to make matchups consistent. This isn't a situation of "Kartana uses Smart Strike and if the opponent goes into Zapdos, it can get paralyzed 30% of the time, this is something the Kartana player must avoid." It's "I can revenge kill this Pokemon, or it can 20% of the time kill my Pokemon back instead, without me even being able to get a turn."
I'd go as far as to argue a Quick Claw with a 100% chance of going faster than an opponent in the same priority bracket, would actually make the item more competitive. Because it would be consistent, so you'd just know that it will occur. Yes this would probably get banned, but that would not make it uncompetitive, just overpowered, which is not the same thing.
So, again. What is the game design reason to keep an item like Quick Claw as is? It is not consistent enough to be something you can reasonably expect a player to, turn by turn, with most teams, punish, or play around. Ursaluna at +2 is going to kill most Pokemon, especially in a Hyper Offensive meta. Will we ban any bulky Attacker because it would be viable on these Pokemon?
Or is Quick Claw just an undesirable item for a competitive metagame?