In the craft-production methods of the pre-industrial world, making enough firearms to outfit an entire army was a challenge. It's not surprising that an armory would see the implementation of all sort of things we now take for granted in industrial production: machine tools, jig & fixtures & gauges, division of labor. It happened first at John Hall's shop in Harper's Ferry Armory in 1819, and spread from there to Springfield. Hall was making a breech-loading rifle of his own design that was more complex and required closer tolerances than the typical musket. There was also an idea in the air, brought over from France by Thomas Jefferson, of making guns with interchangeable parts: this really demanded repeatable machining operations in order to be practical. Springfield ( which had started building guns in 1794) quickly adopted this idea of interchangeability, what was sometimes called Armory Practice, and kept it as a religion for the next century.

Springfield was, however, one factory, if a pretty big one. And as the population got bigger and armies as well, it had a harder and harder time providing enough to equip them. For the Civil War , the Union was forced to buy breech-loading guns from other manufacturers, and import more rifled muskets. And all the special purpose tooling required for uniform parts made big design changes very difficult: in the decades following the War, the Armory would concentrate on perfecting the Trapdoor rifle, improving the cartridge, making more parts from steel, improving the rear sight, but keeping many parts the same in order to avoid throwing away patterns, jigs, gauges..... The result was that, while Europe moved to bolt-action magazine weapons and smokeless powder, the US was issuing to soldiers guns that, at a few yards, looked very much like what soldiers had carried in the 1850's ( and indeed, likely one reason the Trapdoor was used for so long was that the military staff at the War Dept. were happy to see soldiers with something resembling what they themselves had carried in the Civil War)

Which is not to say the Armory could not do something new. It added buildings and staff, when the Krag rifle was adopted. And when the Krag rifle was found to under-perform in the Spanish-American War, the Armory designed a truly excellent rifle, the Model 1903 ( swiping some of the best features from Mauser). But production was still a problem. There were not nearly enough Springfield 1903 rifles on hand to fight WWI, and another model, the P-17 Enfield , was subcontracted out to other makers, like Remington. Likewise, Springfield would make the M1 Garand and M1 Carbine as well as other guns for WWII, but other manufacturers would have to be called upon to make them as well.

In the years after WWII, Springfield would try to step-up its game , designing cutting-edge small arms...but it was becoming rather obvious that in-house design and manufacturing was pretty obsolete. The US government did not own a factory to design and build its own jet planes or tanks...why should it have one to build firearms? The question was very pointedly asked by Defense Secretary Robert McNamara. He knew manufacturing: he had been at Ford after WWII, and had helped to greatly improve their planning, design and management of automobile production. He saw Springfield as an anachronism. And, really, it was: the entire world had adopted Armory Practice to make everything from automobiles to can openers, and so there was no longer a need to have an actual armory to build guns. Just defense contractors.

The problem with this question is that it leaks straight into the sort of debate which his not historical, but rather the armchair posturing of firearms enthusiasts.

The short answer is that the US Army's firearms procurement was fundamentally dysfunctional, and favoured (a) tradition and (b) shooting competitions over actually producing and issuing firearms which were optimal for combat.

After the second world war, everyone apart from the US realised that the then-current rifles were needlessly over-powered and difficult to use. During the second world war, the dominant cartridges were 30-06 (US), 8x57 Mauser (Germany), 7.62x54R (Russia) and .303 British, all very similarly sized and in most cases having their origins in black-powder cartridges which then became extraordinarily powerful when filled with smokeless propellants. All had served in the first world war as well, and were suitable for heavy machine guns, aircraft weapons and other long-distance, high-power applications. They would shoot reliably (both in terms of punching a hole in paper and in terms of punching a hole in a human being) out to a 1000 or more yards. They were also difficult to shoot because of their high recoil, heavy in quantity, and unusable in full-auto in any rifle-type weapon. The alternative infantry weapon to a full-sized, full-powered rifle was a submachine gun; chambered in a pistol calibre, these had much shorter effective ranges.

The British had been exploring an "intermediate" cartridge, .280, after the war, inspired by the German 7.92x33 (7.92 "Kurz", or short) and the Russian 7.62x39. These could be used in what became assault rifles: weapons that could do the job of a rifle out to about 600 yards, had ammunition that weighed half what the full-sized cartridges did, and were controllable in full auto. But after a lot of political posturing, NATO standardised on the American 7.62x51, which was very similar in size, weight and performance to the previous .30-06. The Europeans thought a deal had been reached that if they agreed to 7.62x51, America would adopt the FN FAL (originally chambered in .280 British, but adapted to 7.62x51) but in the end, the Americans adopted a warmed-over WW2 M1 Garand, the M14, in a warmed-over WW2 chambering, 7.62x51.

The result was a weapon which was usable for target-shooting (although subsequent sniper weapons were nightmarish to keep in tune, and couldn't be field stripped), and had lot of traditional walnut furniture, but wasn't usable in full auto, because of the recoil and the weight of the ammunition expended. There is another political story to tell of how the US Army establishment attempted to result the arriving the Armalite AR15 via the Air Force, but eventually the US Army (with some reluctance) abandoned the M14 and adopted the new M16 (a militarised AR15) in the new 5.56x45 (.223).

That left Springfield as (a) manufacturers of weapons of a past age, with walnut and hand-fitted parts and the processes of the 1930s in (b) an obsolete range of calibres with (c) an irredeemable association with what amounted to a corrupt procurement process, aimed at acquitring traditional weapons. The world had moved on, and they had attempted to resist. They lost.