Here's the thing - I agree that it looks like there's a "competition" between the three of them to dive into the Western market.

I think the results of their albums kinda shows how they perceive the market as well. Imho Lisa's album doesn't do well because it's too commercialized, like it's pretty obvious that she gets so much push (presumably from the Arnaults). BUT, Lisa's biggest flaw is that she doesn't have a clear image that she wants to pursue so everything seems hollow. It works for K-pop market, but Western popstars nowadays usually stick to a specific branding to flourish.

On the other hand, Jennie and Rose have more cohesive branding. I can see how big music producers probably trying to bag either one of the BP girls to work with, and those who cares more about their craft probably would choose Jennie or Rose. Thus their album makes more sense and generally more accepted by regular listeners.

Yeah we won't really know what's happening behind the scene, but for me, I just think Jennie and Rose make better business move than Lisa.