BR actually does use the space on the outside between the handle mechanism. They add a little center pocket. About the size of an umbrella pocket. I think it would be really smart to actually make these pockets bigger and to make them removable (yet still so securely fastened that you could check the bag).
I think, Mellon, the virtue of your theory is that you imagine the outer rectangle box as a result of the maximally protruding elements of a bag, notably its wheels. They need to protrude or the bag cannot roll. However, the handle mechanism doesn't need to be in line with the axis of the wheel(s). The more I place the handle system towards the outside, the more space I gain inside - if the other parameters don't change.
I think the ideal solution would be to actually have the entire back of the bag so far out that it is line with the back part of the wheels. Thus the wheels would only protrude from the bag on the bottom. The problem with this is that that would possibly making the bag inoperable because there is not enough clearance to tilt it. This could be overcome with a strong spring mechanism that pushes the wheels out as soon as the bag is tilted. But when you lay it flat the wheel are in line with the back of the suitcase.
Should I get that patented, now.
Till