I definitely don't believe Americans are writing Korean songs. They do the whole shot in cookie cutter Korean then randomly do a sentence in English
You'd be surprised breh, a lot of black Americans are at these writing camps. The demos are in English, and if those demos get selected, the labels will come in and change that into Korean. Even down to how it's sung, flows and all, they keep most if not all of it. Of course, it doesn't mean that every song that comes out of there was produced or written by a black musician, but some of the more R&B and Hip Hop-focused stuff has our touch, more often than not.
As a matter of fact, they're just now starting to hop on the trap beat wave more. There's still the EDM stuff they hop on, but a lot of the newer acts that are coming out? They're on trap beats. On top of that, Dem Jointz has been getting placements over there pretty consistently there too. For example:
This group is from Hybe. Scooter owns the North American branch. They're brand new, and this song was pretty popular on TikTok (I know, I know).
This is a Japanese group that promotes heavily in Korea. They're also brand new.
Now there are of course many examples of them doing cookie-cutter songs with the occasional random English word or sentence thrown in, that much is very true. And I think that happens because it sounds "cool" to them, a stylistic choice for the audience it's meant for. But these companies in South Korea are seeing the dollar signs internationally, and if they're smart, they'll pull back on stuff like that.
BTS Label Owner HYBE Merges With Scooter Braun’s Ithaca Holdings for $1 Billion (EXCLUSIVE) <- This was in April 2021. I wouldn't be surprised if the Kpop industry saw a huge boost during the COVID pandemic globally and are making moves accordingly due to that. And with BTS doing their mandatory military enlistment until 2025, Hybe is probably wanting to make sure they're not on an ice pack during those couple of years until all of the members return.
But to tie it all back... Americans definitely are present in the Kpop industry, because Kpop as a genre is heavily inspired by what goes on here. But it also goes without saying that there's also a huge difference in that how society works in Korea is not the same as how it works here in North America, and that's undoubtedly going to show in the music, regardless of the influence or who's behind the pen and boards.