Romances deal with the important things in women's lives - birth, death, love, the continuity of the species. They are based on archetypes that are cross-cultural in theme and image; Japanese and Hungarian, Korean and South American, Turkish and African women all enjoy them.
Many of the so-called clichés of romance - the abandoned child, the forced marriage, the abduction of a woman by a powerful, potentially brutal man, the taming of such a man by love - are rooted in the cultural and mythic history of every culture, not just those of the Western world. And they have become archetypes because for untold centuries they were a part of every woman's experience; she may not have been forced to marry a man herself, but her best friend almost certainly was.
Think of the battle of the sexes. Shakespeare used it in The Taming of the Shrew. If he wrote it today he'd almost certainly be told to "tone the hero down, because modern audiences would find such a devious, fortune-hunting hero repugnant". Which misses the point completely. In the battle of the sexes it's the man who has to put all the effort into making the relationship work. The woman has no intention of helping him at all; in fact she's actively unco-operative. Which is a pleasant change from life as we know it.
Psychologists agree that it is women who put the most effort into relationships, and this does not mean just romantic or marital relationships - it means all those ties that reinforce kinship and friendship, all the bonds that hold society together. (Who writes to the children in your family?)
You can see why the battle of the sexes myth is so alluring and subversive.