The reloading manuals use the same pressure limits for all three and the 338-06 always leads the velocity race albeit by a small margin. While your theory is correct regarding the ratio of bore diameter over case volume it does hit a point of diminishing returns as with the Whelen.
so you are saying that the 30-06 case becomes more efficient as you increase bore diameter, until you go beyond 338 caliber, whereupon efficincy decreases? Interesting.