From about 1871 to 73 the U.S. Army did use the .44 S&W American in the S&W #3 revolver. It was also used in the Merwin & Hubert Army revolver. This was an outside lubricated black powder round that was later also loaded and sold commercially till about 1940. A 205 or so grain bullet at around 700 fps.
The Army also used the 44 Colt at the same time frame, 1870-73, in the cartridge conversion of the Colt 1860 percussion revolvers and the Remington Model 1875 Army revolver. This was also an outside lubed bullet. Used by only a few years by the Army it hung around on the commercial market till about 1940. It held about the same weight bullet as the 44 American at about the same velocity.
Seems (meaning I'm not sure) that the military wanted to standardize on a heavier bullet and higher velocity of modern design and the 45 Colt (and the Schofield round) fit the bill better than the available 44s.