The .30-03 was actually the US service cartridge for several years, and was itself a refinement of an even earlier .30-01 cartridge, which had all of the dimensions of the .30-03 except for a much thicker rim.
Two things happened that resulted in the case being reduced in length slightly (neck length):
1. Adoption of the lighter, much shorter, pointed "spitzer" bullet, mirroring advances in Germany and France, and
2. Continuing development and refinement of the early smokeless powders.
.30-03 ammunition was loaded commercially at least into the 1930s. Winchester used the case as the parent for the .270 Winchester round, so if necessary, .270 cases can be expanded to .30 caliber and used successfully. They may be just a tad short, but they'll be a better option than a .30-06 case.