Bart B. wrote, "A 1:10 twist for the .30-06 started back in 1903..."
Actually before that, and even before the Krag was adopted. As usual, they experimented with the cartridge before choosing the rifle and began testing .30 caliber cartridges in 1889, using Model 1888 actions. Why .30 caliber? Because, the man who selected it told a reporter, "it seemed like a nice round number".
Things were less formal in those days; under today's system, they would still be holding meetings to choose a new rifle caliber and the "trapdoor" would still be in service.