The Schofield came into military service in 1875 and was chambered in proprietary .45 Smith and Wesson caliber, a shorter round which chambers in the SAA. But the "long" Colt cartridge will not chamber in the Schofield. This created problems in the supply chain and I believe is the reason the Schofield was declared surplus after only five years.
While the 'Schofield' was retired, the cartridge that fit both was not. So, the supply problem would only apply if going to civilian sources for ammunition.
Also, while the .45 Colt cartridge used in the trials was the 255gr bullet over 40gr of BP, I could find no evidence it was issued to the troops. Certainly by early 1874 the Army Ordinance Department had reduced the loading to a 250gr bullet over 30gr BP. Most, civilian ammunition suppliers offered both the 40gr and 30gr loading until the BP loads were phased out in the early 20th century.
On August 20, 1974 the Frankford Arsenal stopped production of the .45 Colt revolver cartridges. Then in early 1875 the Government "Revolver Ball Cartridge, Caliber .45" was introduced. The case of this cartridge was shorter, with a slightly wider rim, as to fit in both the Colt and S&W. It used a 203gr RNFP bullet over 28gr BP. Around 1882 the cartridge was changed from Berdan to Boxer primer. Finally, the M1887 Ball Cartridge was issued, again a compromise cartridge, and was the sole Government Cartridge until it was replaced by the .38 Long Colt iin 1892.
The Army's using the reduced loading compromise cartridge is better understood if the physical requirements for Cavalry recruits is looked at. Cavalry recruits were restricted to able bodied men of good character, between the ages of 16 to 35, between 5'5'-5'10" in height, and weighing not less than 120 and not more than 155 pounds.