There has been a lot of misunderstanding about magazine cutoffs, some of it put out in recent books describing mules hauling tons of ammo through the mud and other, well, stories.
Back in the day, as they say, the "wastage" of ammunition in general was not the big concern, though of course it was (and is) always a consideration. The concept was to fire on the enemy in the single shot mode while "holding the magazine in reserve". In reserve for what? Well, remember that was the 1890s for the Krag and the very early 20th century for the 1903. At that time, the big concerns of infantry were a cavalry charge and a flank attack. Either required accurate rapid fire to avoid being overrun.
So the concern was not so much to save ammunition in general, but to keep it in reserve for specific tactical situations. It didn't matter how much ammunition was in the supply wagons, or in the crates, or even in the cartridge belts; when extra ammunition was needed in a hurry, the best place for it was in the magazine of the rifle.