I think I know why Korean music is full of beautiful and powerful ballads:
The Korean penisula has been the center of area and world conflict for
most of history - Goguryo-Chinese wars (244, 598-613, 645-660), Mongol
Invasions (1231-1259), Japanese invasions (1592-1598), Manchu invasions
(1627, 1637), Japanese colonisation (1910-1945), Korean war (1950-1953)
and even the continuing civil war.
War brings much destruction and loss of human lives, property and loved ones. To overcome such sadness and loss, songs about loss and struggle brings empathy for those who remain. Ballads are a cultural and historic relic, echoing a confucian ideal - Living closely together, assist each other, and have compassion and be considerate of others.
"As long as we all come together to overcome hardships, we will never lose sight of our hopes and dreams..." Marriage, relationships, and friendships - a highly socially structured and conservative society.