Look at the ballistics of the .270 and 30-06. The .270 is flatter shooting when you compare bullets of similar weight.
I think it boiled down to we had a lot of .30-06 ammo, and didn't want to change. Note that the US military is still looking at .270 or 7mm bullets for their next cartridge. The 6.8 SPC for instance.
“I think it boiled down to we had a lot of .30-06 ammo, and didn’t want to change.”
Precisely. The US military was sitting on tens of millions (if not billions) of .30 M1906 rounds left over from World War I. And per standard governmental procurement practice of the time, existing supplies had to be used up before a new design could be implemented. (Which is also why other interwar developments, such as the improved M1 .30-06 cartridge and the pistol-grip stock for the Springfield rifle, were not introduced until almost the eve of World War II. The leftover supplies from 1918 had to be used up first.)
Military spending in the 1920s and 30s was dismal at best (this was the optimistic era of “no more war” sentiment and the Kellogg-Briand Pact), and the military visionaries who saw the value of a semi-automatic rifle in future battle realized they would have a hard enough job trying to justify the money to replace millions of Springfield and Enfield rifles. Justifying new ammunition as well would likely have been a non-starter for the whole project.