Multicultural roots of Western culture may have made integrity an important signifier of trustworthiness. Even going back to Shakespeare, you saw the theme of split identities everywhere in Western literature, and most of Shakespeare's villains are noted for their two-facedness.
The modern day implication of that cultural legacy is our cult of authenticity. For a rap singer to be taken seriously by his peers, he has to be "real." The realness is a hard earned credibility by showing a singular identity, and not being perceived as the real thing for someone immersed in that culture would be the equivalent of "losing face" in Eastern cultures. Something akin to social isolation and even death.
Another, perhaps more relatable example, is something I often hear Americans say. It's said that in America you can be who you say you are. That is at the heart of the open society for which Americans are praised, and Americans take your word at face value, until you say or do something contrary to their expectations of your self-proclaimed "role."
So thinking over what I wrote, I think the reason why role-playing works in Japan and doesn't in America is because Americans have a culture of self-invention, a culture built on appearances, they also have a wariness about being taken in by people who change their appearances often.