On the one hand, yeah definitely export your own cultural weirdness. Part of the joy of having so many other cultures in the world is getting little peeks into them via art.
On the other hand, some of my favorite games of all time have come from Japanese developers fetishizing American culture and trying to pretend it's normal. Deadly Premonition, Metal Wolf Chaos, all the works of Hideo Kojima. I think there's something to be said for the strange fusions that can occur when an outsider makes art in the style of a different culture.