I've never understood why love triangles are such a thing in kdramas. I don't date so I don't know about real relationships but is there some kind of weird desire people have to be in love triangles so they want to live vicariously through characters?

I honestly cannot see the appeal. If you're in the center, there's all this attention on you and eventually you'll likely have to break someone's heart. (Though I guess if you're into attention, one would like that) If you're the pursuer, you have to watch the person you're interested in becoming more attached to someone else which would/could just breed jealousy and resentment. All those heighened emotions.

But the main thing is there are so many people who exists, why fight over one?! Is it really that hard for people to find other people they are attracted to, whatever the attraction is (be it aesthetics, personality, temperment, etc)?

There was only 1 time when I didn't mind the love triange in a drama and I think it was mainly because I never ONCE considered it a triangle and that was the drama Start Up. I didn't even know about second lead syndrome at the time but I learned that show is always listed under that.

While there is definitely TONS of melodrama in Empress Ki, when kdrama melos are discussed it usually means MODERN melos (our times and all the way back to mid-20s century max), not sageuks (historical dramas about Joseon and everything before that) which are the genre itself. Comparing the two is rather pointless, that's how different they are. So when the show is sageuk, it's usually primely sageuk and only then something else - romcom, melo, palace intrigue, detective, fantasy etc. But when it's a modern drama, melo is mostly just melo, unless some other genre is added to the mix. But it's still usually considered as a melo first and foremost. It all may sound complicated, but it's actually not, trust me)))

Samples of the melodrams that were really popular back in the day among the big3 are Autumn in My Heart, Winter Sonata, Sad Love Story, Stairway to Heaven, and I'm Sorry I Love You. There are more but I can think only of these at the top of my head.