I'd love it to take on an ARG spin. It would make the mail-in factor more impactful, I'm pretty sure, as you're no longer "just playing a game" by mail (though that would no doubt be fun too), you're instead taking part in something bigger, something "real" by sending your letters.
I don't think it would be very limiting either, except in the area of setting the player's role. It's way harder to give the player a backstory (like "you left your country"), since each player will of course have their real memories. It can still be done, however, with some memory loss thing or maybe a backstory the player wouldn't know about ("when you were a baby you were moved..."). Except that one point, though, an ARG format would probably not be especially limiting.