Let's pretend for a second that the US Government were completely insane and tried to do what you described.  It's hardly going to be a "backed" currency if they're constantly printing a greater number of dollars whilst at the same time dividing the number of bitcoins they're "backing" them with into smaller and smaller fractions.  Your entire premise is utterly moronic.  It would only serve to draw more attention to the fact that the value of the currency is constantly diminishing.  But please, keep arguing semantics about how fractions of a whole are magically greater than the whole.