Perspective from a Korean-American who grew up in Korea when I was younger.
The “dead fish” or “pressed-lips” kiss scenes are not strange to me at all, and it actually seems natural. I can virtually hear/see the gasp or tsks or shaking your heads. 
I know Korea has changed so much past 30 years or so, and passionate kiss/love scenes (both on TV and in real life) are becoming more common and accepted.
But I grew up in an era where there was absolutely no PDA (public display of affection). I don’t believe any of us (people in my generation) has ever seen our parents hug (let alone kiss!) in front of us or see random strangers displaying any form of PDA. I remember one day when one of the sunbae unnis that I know was telling us a story about how while she was walking by a dark alley, she heard a couple talking in a hushed voice, and then she actually heard the sound of a peck! Dun-dun-dun!! That was literally the juiciest “dirty” story we heard at that time! lol
Kissing scenes were never shown on TV. If there was some kind of romantic relationship forming, the ML and FL may hug and their faces will slowly get closer to each other and when their faces are about 2 inches apart (~5 cm), the scene will be cut abruptly and they move on to the next scene. So the viewers can just assume that they must have kissed.
Then in the early 80s, I was watching some Korean drama and this was the first time the ML and FL’s lips actually met for less than 1 second to show the actual kiss. Well, it was more like a quick peck, but I was still SO SHOCKED that they actually broadcasted it! I don’t remember when I first saw open mouth kissing (aka “French kiss”) on TV, but my initial reaction was that it was pretty disgusting to show that. Like who wants to see some actors’ tongues working that way?!
I know that Korea is a lot more westernized and open about this kind of things now. But even now, there’s some stigma about participating in passionate kiss/love scenes. It’s more acceptable for the guys, but if the girl is a really good kisser, then some may see that girl as being easy and “too experienced.” I think a lot of FLs in the dramas are supposed to be naive and innocent and not have a lot of success in their romantic lives before meeting their destined love of their life. So they can’t be too eagerly participating in the kissing scenes. They need to let the ML take charge and they need to show they have no idea what to do. It’s almost like their innocence is being taken away, and it can’t be rushed. I still think pressing lips kiss, without opening your mouth, is romantic, too.
Regarding the “dead fish” look: I believe it’s portraying the shock the girl is feeling when she is being kissed (maybe for the first time in the drama). So instead of “enjoying” it, she is too shocked about it. It’s especially true if the FL is not mentally ready to commit to the ML yet.
Also as Korean actresses, they have to be acting with many different male actors in different dramas, and if they kiss “deeply” so much with so many guys (albeit it’s just acting), it might affect her real relationship. I know, I know. Some of you may want to protest and say, she is just doing her job and you shouldn’t date/marry her if you are bothered by that! But I am just telling you that’s how it is.
Korea is still a very conservative country and not everyone participate in physical intimacy until they become older.
The funny thing is, although Koreans in Korea are “progressing” more, Korean-Americans are even more conservative in many ways. You can see Steven Yuen doing the “dead fish” kissing in a popular American show. He is just portraying how “shocked” he is at the beautiful girl’s advance on him, that’s totally his “Korean-ness” coming out of him. 
https://www.youtube.com/watch?v=tgxyr1A4ob8
It was actually really funny and interesting to see/read the viewers demand better/longer/earlier/deeper/passionate/steamier kissing scenes when I first joined Viki and started reading the Timed Comments. The pace was perfectly fine for me, but the international viewers were being so impatient! At least that’s what I thought! lol
Some of the latter shows (like Queen Inhyun’s Man & What’s Wrong with Secretary Kim) showed really good kissing scenes and I know the viewers were ecstatic about them. I didn’t mind it, either. But I would not have felt comfortable if I were watching those dramas with my family. Luckily my family weren’t interested in K-dramas until last year when we were quarantined at home and had nothing better to do. So we watch more as a family now. But my husband fast forwards all the steamy/passionate scenes when our teens watch with us. He even comments, what’s with these K-dramas that are showing too much now?! lol And we are the type who actually hug and even kiss (actually a peck - or “pressing lips” according to you all ) in front of our kids all the time.
Welp, that’s it from me. 