Idol groups who attained success by breaking the mold and fitting the mold

Blackpink broke the mold in that they were global stars designed to appeal to English speaking audiences. Two foreigners, one Thai, three English speakers. They just dont give off a Kpop vibe. And the way they changed the way Kpop idols are viewed (from dancers to fashion icons and influencers) made them stand out as well. They were Kpop's first global celebrities, not just idols.

They also engineered the last cultural reset in Kpop with their unique brand of EDM trap girl crush. We are finally in the midst of another one with New Jeans.

Quote from BlackpinkHouse

Blackpink broke the mold in that they were global stars designed to appeal to English speaking audiences. Two foreigners, one Thai, three English speakers. They just dont give off a Kpop vibe. And the way they changed the way Kpop idols are viewed (from dancers to fashion icons and influencers) made them stand out as well. They were Kpop's first global celebrities, not just idols.

They also engineered the last cultural reset in Kpop with their unique brand of EDM trap girl crush. We are finally in the midst of another one with New Jeans.

They didn’t do anything unique. They just outdid everyone within already existing tropes in kpop. They didn’t even do anything that different than what 2ne1 did except be prettier and more charismatic.

me when I see ethnic hip

You forgot ATEEZ, there is no other group in KPop who sounds like them. They came from an unknown company and still menaged to become very big and sucessfull.

And there are no other "Cowboy pirates" in KPop

SNSD destroyed the moulds and revolutionised the industry in many ways

A gg with more than the usual 4-5 members was seen a joke but now is a completely normal part of Kpop

Multi media entertainment focus esp TV was a core part of their appeal.

Members branched out really early on into other careers like acting, TV or modelling which has allowed them all to still be very active individually 15 years later when majority of their peers have left the spotlight

One of the forefront pioneers of hallyu worldwide.

Not something they did directly but many idols became idols because of SNSD, companies created their own copies of SNSD and trained their idols to SNSD routines.

Your definition is quite subjective and can differ regarding to people.

For example, some K-pop hater could say that no one broke the mold since they "just copied the US pop artist" (according to them).

And I like pasta.

Quote from BlackpinkHouse

They also engineered the last cultural reset in Kpop with their unique brand of EDM trap girl crush. We are finally in the midst of another one with New Jeans.

in the same way NewJeans took “b-side material” and refined it to moments of perfect pop, BP isn’t doing anything brand new with the trap beats

The most musically interesting moment in their debut singles was that random country music pre-chorus just before Whistle’s chorus. Pure teddy genius. But the trap? Absolutely everywhere even by 2015

For me it's bigbang. They broke the mold into pieces. First recognized self-composed idol, using the lightstick or scarf for fandom instead of colour, never focussed on choreo, they are loved for their music (that's why they still can chart well despite all the controversies)

Mamamoo did by live singing actually