Despite weapons such as the Spencer, Henry, and Colt repeating rifles coming on to the scene with impressive magazine capacities during the American Civil War, the US Army failed to adopt a standard rifle capable of firing more than one shot at a time until the Springfield 1892 Krag. Why didn't they make a rifle like the Henry standard across the army after the Civil War? Wouldn't the single shot 1873 "Trapdoor" Springfield rifle be a step back backwards from repeating rifles of the time?
You might be interested in this answer by u/Bodark43 and this one by u/Meesus who have covered a very similar questions previously.
A variety of reasons, really. There was a general reluctance by militaries across the world at the time towards the adoption of magazine rifles - especially in the US - and the postwar US Army had a severely limited budget that was chiefly focused on demobilizing and modernizing efficiently.
The doctrinal concerns over magazine rifles seem unintuitive until you look at the strategic realities of the time. Logistics were a huge concern for armies of the time, especially one like the US Army that was campaigning over fairly large distances during the war and fighting on remote frontiers after the war. Armies all over the world were concerned that magazine rifles would cause poorly trained troops to waste ammunition in a panic, and the potential for soldiers to outshoot their supplies wasn't just theory, it was something that was demonstrated by Union forces during the Battle of Chickamauga. During that battle, a unit armed with Colt revolving rifles held its ground while the rest of the army collapsed around it, but in doing so exhausted their ammunition supplies (and some brought during the battle to resupply).
Rifles like the Spencer and Henry suffered from weaker ammunition - the Henry in particular firing an anemic cartridge that rapidly lost effectiveness beyond ~100 yards. The Trapdoor carbines would use down-loaded ammunition, but for infantry rifles, the Spencer and Henry's ammunition lacked the power the Army was looking for in an infantry rifle.
There was also the mathematical realities of it. Prior to the advent of speed-loading devices like charger clips, magazine rifles on average don't significantly increase fire rate over long periods, as loading the whole magazine one round at a time isn't any faster than loading and firing individually.
As for the specific decision to go with the Trapdoor Springfield, that had to do with the economic situation after the war. The Army recognized the need to replace its rifled muskets and standardize on a more modern cartridge-firing rifle, but its budget was severely limited Congress. To adopt a modern rifle, they opted to pursue a design that would be a cheap conversion of existing muskets, and the Trapdoor was the result of that. This push to standardize the inventory was strong enough that cavalry units equipped with Spencers even had their repeating rifles replaced with single-shot Trapdoor carbines.