I think another approach to handling this is to consider how universally applicable the "hax" is. I have less problems with things like Serene Grace, (post weather-nerf) Sand Veil/Snow Cloak, Quick Draw, and Leek, because those abilities & item are only applicable for specific Pokemon and/or are limited by specific conditions, which makes them easier to handle on the spot. If any abusers of these abilities turn out to be problematic, we usually look at the abuser(s) itself rather than the general ability. In cases where those Pokemon start to stack other "hax traits", namely Serene Grace + paraflinch, or Scope Lens + Focus Energy, it starts to feel less like "hax" rather than a deliberate strategy that the mon is working towards. On the other hand, I have more issues with the likes of Quick Claw, Brightpowder/Lax Incense, and Focus Band because damn near everything could use it to similar effect.
From a counterplay perspective, it's also important to assess how practical the counterplay is, or how much the problem strategy outnumbers the counterplay. For example, we have Evasion Clause not only because most of the counterplay (never-miss moves) are too weak to be good counters or can simply be responded to by the right evasion abusers, but also because Double Team can be learned by damn near everything so the evasion user will always have more options than the defender. The same went for Swagger too; everything learns Swagger, and the Swagger user could just counterprep your Swagger answer by running a Swagger mon that beats it. Conversely, we've never touched upon accuracy-drop moves since the counterplay is as simple as just switching out. The more specific hax-enablers, like the aforementioned Serene Grace and friends, at least can be seen coming so you can better position yourself against it, and even more general hax situations like 'paraflinch' needs some effort to be executed.
This leads to my stance on King's Rock overall. While it is a 'general hax-enabler item' like Quick Claw, Brightpowder, and Focus Band, it differs from them in the sense that it has a prerequisite to be useful: the holder needs to be faster than the target. That criteria alone limits the potential users of this item to faster but consequently frailer Pokemon, which can make the list of King's Rock users more vulnerable to practical counterplay options such as priority or status (particularly paralysis, though burn also cripples most of the better King's Rock abusers). Speaking of abusers, Cloyster is more or less the only one even worth worrying about, since it's the only one with a good speed-boosting move as well as guaranteed 5 hit moves that do not make contact. Other King's Rock users do not approach the consistency Cloyster has; Weavile's multi-hit moves have inconsistencies that can be worked around (Beat Up requires a deliberate team structure and none of those mons can be statused/KOed, while Triple Axel is unreliable), Urshifu-Rapid-Strike has infamous issues against contact punishers and fat Water resists, and lol Cinccino, etc.. Even the argument of "King's Rock being an item that has no place in competitive" feels weak when Stench, despite functioning similarly to King's Rock (but does not stack) and has users with multi-hit moves, is left alone because its abusers are not at all noteworthy, proving that we also acknowledge the effectiveness of the abusers when trying to ban something simply for being "uncompetitive".
To me, this feels like a clear case of the Pokemon being the one to break the item, not vice-versa, so tl;dr: King's Rock is not on the same level as general hax items like Quick Claw/Brightpowder/Focus Band (which should be banned) since it's more restrictive and easier to counterplay against, and with Cloyster being the only real problematic user of the item, there feels like there is more basis to ban Cloyster than to ban Quick Claw tbh.