It would have been designed around the issue ball .30-06 ammo of the day (1917), which of course is .30 M-1 ball, introduced, unsurprisingly in 1906, as a rapid response to the Germanintroduction of THEIR ground-breaking, 150 (ish) grain, flat-based spitzer bullet that essentially rendered all other contemporary military rifle bullets obsolete.
Interestingly, the .30-06 "barrel spec" retained the 1:10" twist requirement from the ".30-03" with its original LONG, heavy, round-nosed bullet.
Conveniently, the P-14 in .303 has a 1"10" twist, so that was one less set of production tools to modify or replace on the shed-full of Pratt and Whitney sine-bar rifling machines.
As long-range machine-gunning became a serious battlefield tactic, a heavier, spitzer bullet was introduced, the "M2". The Germans had done the same thing with their 7.92 x 57 sS round several years earlier. See also the Britishdevelopment of the mighty .303 Mk 7 and the Swiss
for their superlative GP-11 cartridge with its extra-slinky boat-tailed bullet. (A "battle" bullet designed and made by watchmakers).
Thus, the service .30-06 barrel in all manner of platforms retained the 1:10" twist of the original .30-03, whether it needed it or not.
Note that the subsequent 7.62 NATO went with a 1:12" twist, because it was sort-of standardized with a 147gn boat-tailed FMJ that would happily stabilize in that twist, at all temperatures and elevations. Initially, if I recall correctly, Britain and Australiawent with a 144gn BTFMJ and a slightly different loading (L2A2) that was "outside the NATO spec." and thus did not have the little "cross in a circle" stamp on the head.