I have thought about ideas of culture and cultural influence in BattleMaster for a while now, but what you describe here is not something I think I would be interested in implementing. Each region already tracks how much they like every realm on the continent—it's called sympathy (or, for the realm that owns the region, loyalty). And we don't need more ways for big, strong realms to win more easily.
If I were to implement culture, it would only be on a new island or a complete reset (probably not the South Island, because the idea doesn't go too well with its War Island nature), and it would be giving culture to the peasants and minor nobility—or rather, cultures. Several distinct native cultures, with nobles created on the island having the option to come from one of them or not, shifting as populations shift, having greater or lesser affinity for the realms on the island. Ideally, it would (somewhat as Zakky suggests) go along with an overhauled idea of religion, one that is much less player-driven, such that each culture has opinions on each religion.
That would provide an organic basis for conflict between player desires and the wants and needs of the NPCs they rule, something much more interesting than just another stat to maximize by doing what they already want to do.
