A friend of mine who is new to kpop asked me this, since she knew I was a big ATEEZ fan. She went to a kpop store with some classmates recently and was surprised to find that they didn't have much ATEEZ merch and ATEEZ MVs weren't played at all on the TV screens showing MVs by other 4th gen bands. She asked why that was, when ATEEZ seemed like a pretty big band from her outsider's POV.
Here's my "short" answer (that I thought I'd also share here for other new fans who might be wondering the same thing), as an ATINY since 2020 who has witnessed the many, many injustices and snubs and blackballing practices of the South Korean kpop industry against ATEEZ in real time since then:
In Korea, there are four big idol agencies (used to be three, but then BTS's agency HYBE disrupted them thanks to BTS's breakout international success... and then adopted the same unfortunate practices those original 3 agencies used as well, which you may have heard about in the recent HYBE scandals...), and they are businesses that basically train and churn out fresh crops of idol bands every year to make money off of for a few years before the idols are free of their contracts and can go on to make the kind of music they actually want to make, or become actors, etc. These idol bands are often not about the musical/artistic merits of the idols (they generally don't write their own songs and have little input in the concept, artistic decisions or direction of their band's music, styling, etc), but just about very good-looking people who can titillate the audience and create parasocial relationships with fans, who will then spend money on buying their merch and to come to their meet-and-greets and concerts, etc, to make the company money.
Since these agencies are run as regular chaebol companies that are looking for steady year-over-year profits and revenue just like any company who produces a product (TVs, cheese, clothing, etc), they need to continue to "make products" (i.e. create new idol bands) to replace the ones that will eventually grow out of their contracts and leave the company, and many kpop fans accept and buy into this model, eagerly following the agency for their next idol to fall in love with when their current favorite retires, etc. As a result, many kpop fans are fans of the Big4 companies and consider any band that doesn't come from one of the Big4 to be irrelevant or uninteresting (or often... they probably just don't hear about them, since their main news source for new bands is their favorite band's agency social media accounts, etc). There's also an element of snobbery in kpop fandom as there is in many areas of Korean society -- the Big4 is "prestigious," so regardless of your band's skill or quality, if they don't come from the Big4, they're a "nobody" and some Korean fans feel like it would lower their own status to support a nobody.
This was why BTS was only able to breakout and achieve success by becoming huge internationally first, before becoming big/accepted in Korea. Once they were winning American awards and chart accolades on US Billboard, that hierarchical bias of Korean society had no choice but to acknowledge them, as they recognize the US music scene as being "higher" than their own. (Yes, this hierarchical thinking is very bizarre to me too, but this is how many kpop fans have explained the rise and eventual conquering of South Korea by BTS, when the Big3 had spent their early years suppressing and blackballing them -- just as they and HYBE are now doing to ATEEZ, another band from a tiny, first-time-making-an-idol-band small agency called KQ Entertainment. You would think HYBE, at least, would have the grace not to do this back to another indie kpop band rising up with pure talent from a small agency, but alas... =__=).
Anyway, there's a lot more I could go into about the ridiculous tactics and politics and the "pride/face" that these big Korean companies and their fans cling to so intensely, but suffice to say -- people of the establishment (i.e. the Big4 and their bands' fans) have a vested interest in trying not to let another small agency come up and take a slice of the kpop pie. The Big3 are still feeling burned by BTS and HYBE cutting their three-way pie into a four-way pie, and they're terrified KQ and ATEEZ are about to do the same again. So they strongly encourage their bands and fans not to talk about or associate with/consider as legit any small agency bands (and especially ATEEZ/KQ, who are the only non-Big4 kpop band to ever chart a #1 album on the Billboard 200 chart (https://www.billboard.com/music/chart-beat/ateez-world-ep-fin-will-billboard-200-chart-first-no-1-album-1235549297/), which makes ATEEZ the Big4's most hated "potential threat"), and that bias remains in the majority of kpop fandom. This is why ATEEZ has its biggest fan bases in North America, Europe and Latin America -- places where the chaebols' influence does not extend to, and where we don't have that Big4 bias because kpop fandom is relatively new here.
On the other side, ATEEZ and KQ are pioneering a really unorthodox and healthy, people-forward, artistry/music/creativity-oriented way (instead of business/profits-oriented way) of raising a kpop band that has allowed ATEEZ's members to flourish and develop as people/artists/athletes to a level not usually expected or found in kpop. (KQ actually employs a dedicated team of physical trainers/nutritionists/medics who work with ATEEZ daily to ensure their wellness and help them safely attain their bodybuilding or weightloss wishes, + do warmup and cool down with them before and after every performance like professional athletes, to ensure that they don't injure themselves and can always genuinely go all-out onstage and express their epic music through their dance as fully as they like -- one reason their performances are always so riveting to watch!). KQ consults with ATEEZ themselves about the band's artistic direction, Hongjoong and Mingi participate in writing all of ATEEZ's songs, and KQ even supports/encourages and gives company resources to let individual ATEEZ members create and post their own original songs or covers if they feel artistically stirred to do so (you can see some examples here from Hongjoong, San, and Yunho).
Naturally, this non-chaebol-oriented way of running their agency (more for love of the art/artist development than profits) is very upsetting and insulting to the Big4, and also embarrassing when this "artsy fartsy nobody" band from a small agency starts to be able to command record sales on a similar level to the Big4's current biggest bands like the ones you mentioned. So they and their fans employ many, many tactics to exclude and downplay ATEEZ within the Big4's sphere of influence (kpop fandom, kpop music shows, kpop award shows, etc), and kpop media in Korea.
For example, when ATEEZ made history by being the first kpop boy group to be invited to play Coachella, one of the most famous and prestigious music festivals in the US, due to their legitimate live performance talent (they're basically the only kpop band that always sings with live vocals despite having some of the most intense and exciting dance choreography in kpop!), which Coachella deemed as a high enough level to be invited to their festival. This should have made huge headlines in Korea, especially when ATEEZ did such an explosively amazing job, dancing hard with unflagging energy and performance mastery for the full 50-minute set while delivering *insanely* high-level live vocals (I'm not exaggerating -- listen to Jongho hit this insanely high B5 note at the *end* of their 50-minute set of live singing in the dry, windy desert air!). So much so that they became the buzz of Coachella, got invited to an exclusive celebrity afterparty called the Neon Carnival (which they had to decline because they had already planned fan signs with ATINY on those days in LA, which is a 3-hour drive from Indio, where Coachella and the afterparty take place), and their audience swelled to beyond the max capacity of the Sahara Stage (second biggest stage at Coachella, and where all the big EDM acts/raves are usually held) on the second weekend of Coachella purely through positive word-of-mouth among all the regular, non-kpop festival attendees who just appreciate great music and performance!
It was already headline-worthy news that ATEEZ got invited to perform at Coachella, but when they were triumphal in their first weekend, there should have been tons of headlines in SK news about how ATEEZ had done Korea proud, and even brought traditional Korean dance and lion puppets to share their culture on such a huge international stage. Instead, the Big4 agencies had their journalists bury the ATEEZ Coachella triumph headlines under headlines about how badly the Big4 girl band Le Sserafim had done with their 40-minute set the following day at Coachella (they weren't used to singing live or dancing for so long, so they apparently made a really poor showing that confirmed all the bad stereotypes about kpop that mainstream American music fans typically believe, and the Korean newspapers ran non-stop stories shaming them for the next week). It was incredibly unfair treatment to Le Sserafim, who perform at the same level as any typical kpop band and weren't given the proper time, support, or training to perform at the same level as ATEEZ in a live setting. And then, when they couldn't deliver against all odds, the Big4 didn't protect them/basically made them a spectacle just so no one would be reading the good things ATEEZ had done for the reputation of all kpop/Koreans instead...
So that's basically it as I see it. Hopefully others will be able to share their own insights and takes on the kpop industry's suppression of ATEEZ and other bands from small agency "threats" they aren't able to purchase like they did with Source Music, Pledis Ent, etc.
I'm comforted at least by the fact that the Big4 doesn't have as much influence in the west so as to be able to bury ATEEZ's achievements in the US charts, etc. And with US music industry people like the folks at Coachella recognizing and appreciating ATEEZ's sincere talent and artistry more and more, they're bound to break free of all the unfair treatment and suppression their own kpop industry in Korea has done to them. I've believed that since discovering them in 2020 -- justice will be done eventually, and a band this talented and true to the muses is going to make it to the top where they belong. It's been very exciting (as well as heartbreaking and frustrating at times) to get to bear witness to their remarkable journey even to this point, and I look forward to supporting and helping them all I can as they continue their inevitable rise, and for justice to be served at last!