I can't understand how this group didn't breakout. To me they have all of the igredients
They have everything except one thing: Branding.
We often say "you can't judge a book by its cover" but in reality this is unfortunately what makes the difference in a society that is more and more connected and where we have less and less attention to pay and this is even more true in industries such as kpop which have a young audience.
There are of course exceptions, but in the vast majority of cases you will see that successful bands have a very strong brand image, and conversely a bad one for groups that are less popular or have lost popularity.
In the case of Purple Kiss, the company literally never created one. There were very abrupt changes in concept between different comebacks and we see that the company tried to surf on trends in a very clumsy way, and all this did was harm the image of the group, which was already nonexistent.
This is just my opinion, but I think the company should have given the group a complete autonomy and let them do everything.
In the songs that the members write there is a certain identity that emerges, it is certainly a little shaky with all these 360° that the agency made the group do, but I think that if they had been free to do everything and choose from the start the image of the group would be much stronger, and would be halfway between a dreamcatcher and a red velvet.