question is, how much of this culture-shaping process is there worldwide.
All the time, everywhere. Things don’t move up organically anymore (if they ever did). Anything that becomes popular enough in the world was paid for, and worked on 8 hours a day by teams of people to make sure you get that content delivered to you.
Kpop only became a world phenomenon after gangnam style. Even after that though it was still kinda niche. Then they recruited talent, made supergroups, made BTS, and now are sending them to the USA. Now Kpop and Korean fashion is even bigger than before, and most teens do either one of the two (either listen to Kpop or get inspired by Korean fashion).
I sincerely don’t believe there is such a thing as organic, or inert if you prefer, popularity. Even “organic” SEO takes human labour and effort.