While I can't speak for Bill, I have had the luxury of seeing him perform this for both laypeople and magicians, in performing situations and in lectures, and as such I will throw out my two cents (or, 1.8 with the current exchange rate).
The box, besides giving you a nice full circle effect (invisible ball of death- or whatever- comes out, flies around, and eventually returns back to the box), it takes the heat of the cloth.
Through the structuring Bill provides, at the end of the effect people want to see the box! It sounds silly to us, but it makes sense on some level- something came out of the box and went back in. What is it?
So, the box, besides adding to the theatrical element of the effect, is responsible from redirecting the heat away from the gimick.
Just my thoughts.