Hmmm. Are you reading "loose nut behind the wheel" to be an analogy for "mentally ill person driving a car"? If I'm not mistaken here, it's an analogy for "it doesn't matter how well you put a machine together if you don't tighten down the bolts." I suggest rereading the phrase with "bolt" instead of "nut" (even though that makes the analogy less perfect) and seeing if it still reads poorly. I think you're misapplying different definitions of "nut."