I know that Greeks obsessed with Latin American telenovelas, and now obsess with Turkish soaps.
My uninformed guess:
Many countries’ romantic dramas feature overt sentimentality and melodrama. They spend a lot of time emphasising the romantic relationship between protagonists, and they do so overtly—music, longing gazes, dialogue.
American soaps feature plenty of melodrama too. But they do not emphasise the romance nearly as much: it is certainly there, but in comparison, it is dealt with in a way that Anglos would say is restrained, and “warmer” people would say is cold. Some music, some longing gazes, but nowhere near as much—much more emphasis on the challenges to the couple. Much less vaseline on the lens.
And obviously this is a Northern/Southern (in European terms) cultural difference.
My guess: Turkish TV is filling a niche of sentimentality unsatisfied by American TV, and much more congenial to Arab and Latino notions of what a soapie should be like.