You would have thought the US military would have put a lot of thought and study into choosing .30 caliber for our small-bore, smokeless powder cartridges, the 30-40 Krag, and the 30-06.
According to Franklin Mallory in his book, THE KRAG RIFLE STORY, the choice was arbitrary, merely copying what most European counties were doing, using from 7.5 to 8mm diameters for their military cartridges at the time.
The Spanish-American War proved the worth of the 7mm bullets (.284") in the 7x57 Mauser rifles, yet, despite serious consideration, the US chose to stick with the .30 caliber when it developed the rimless 30-03/30-06. That American attitude of "bigger must be better," evidently won out.
So, my answer to the OP's question as to the best bullet diameter bullet for the 30-06 case? I would be inclined to choose the .284 bullet, which just happens to duplicate one of the best American cartridges ever produced: the 280 Remington.
