That would make sense if the Mormon missionary dress code constituted a generic vaguely respectable look, but it's a lot stricter than that: more like a uniform, and distinguished from mainstream respectable in several subtle ways. (The thin black ties are what comes first to mind; I've never seen one off of a Mormon missionary or, in one case, a classmate playing Orson Scott Card.) People pick up on that; it fairly screams "outgroup", and in fact it's why we're having this conversation in the first place.

In light of this, I think I'm more inclined to buy the theory mentioned elsethread, that the missionary tradition is meant to produce loyalty in existing members rather than new recruits. If that's what you're going for, you want distinctive identifying features for your ingroup.