According to Alexander Rose in his very useful book "American Rifle" In the 1870 U.S. Army military trials for a new rifle of the 41 entrants into the trials only one was a repeater, that was the Spencer rifle. Winchester, knowing that Army Ordnance disapproved of repeating rifles did not submit any for trial. The army did not believe repeating rifles (rifles that could be reloaded by working a bolt or a lever) were fit for combat. It chose the single shot Springfield rifle which had been used as a muzzle loader during the Civil War and had been converted into a breech loader. It was pitted against the Remington Rolling Block single shot rifle and the Springfield won.
The Armies chosen round was the 45-70 a round too big and strong for the action of any Winchester, Henry, or Spencer of the time. The army considered none of the rounds that could be used in a repeater to be satisfactory. Even a few years later when the 44-40 was introduced in 1873 it was considered too light weight of a round for the Army and the Winchester rifle unreliable for combat. (The debate around these perspectives of the Die-Hards vs. the Progressives was a deep and long one in the military, Rose in his book covers it well I think, a very readable book.)
At any rate the 44-40 as a rifle round was never considered so when the round was introduced in a companion sidearm, the Colt SAA in 1878, the 45 Colt SAA had already been adopted for use in 1875.
The Army favored large heavy bullets. The 45 Colt was a modern cartridge and was heavier and faster than any available 44 I believe. In a gun that was tougher than most others at the time. It was the official round until 1892 when it was replaced by the 38 Long Colt.