I don't see that we have to stick rigidly to one approach or the other. I think there are good arguments for exposing them to structures slightly in advance of what they know, but also fr teaching the rules. Why can't we take a mixed approach? I see nothing wrong with exposing learners to, say, some past tense before teaching it.
I don't think that culture can be completely separated from the language, which is, after all, the main vehicle for a culture. What matters is how we approach the cultural aspects.