In the 1850's, there was a great frenzy of modernizing of arms in Europe, including small arms. Breech-loading rifles were adopted, or muzzle-loading rifles were converted to breech-loaders.The US caught some of that frenzy, but only some. It had done its own breech-loaders ( like the Hall and the Jenks) but was not satisfied with them enough to make them standard issue. During the Civil War, breech-loaders were given to mounted troops ( awkward to re-load a muzzle-loader, on horseback) and some lucky ones bought Henry rifles, or were able to use Sharps rifles for sniping, and some cavalry even got Spencer repeater carbines. But the rank and file soldier still had a rifled musket. Of which around a million had already been produced- it is very hard to quickly equip an army, and Springfield Armory would not have been able to crank out anything new in huge numbers required, even if it had wanted to do so.

In the middle of the War, though, the Armory and the War Dept. knew that they were going to have to abandon muzzle-loaders pretty soon. There were many independent gun designers who were hoping their model would be picked. But Springfield also had one in-house, Erskine Allin. He undoubtedly knew the British had converted their existing Enfield rifles to breech-loaders with the Snider design, and when the War Dept. announced trials for a possible breech loader near the end of the Civil War in early 1865, he quickly had some of his own conversion designs ready for them.

If the prospect of making a new kind of gun was daunting, it was doubly daunting for Springfield, because it had adopted the American System of manufacturing, where as many parts of a gun as possible were interchangeable. To do this required a lot of specialized jigs, fixtures and gauges. Any great change meant discarding a lot of those. Also possibly to be discarded were a huge number of rifled muskets left over from the War. Although many very good breech-loading designs were submitted, like the Remington Rolling Block and magazine weapons like the Henry,once the trial were done in 1866 the Armory pushed for the Allin Conversion and the War Dept went along ( conveniently since Allin refused to ask for them, royalties didn't have to be paid). The conversion of the rifled-muskets turned out to require not one but several conversions. Finally the Armory came up with something new, that looked and acted like the Allin Conversion, but had few parts of the old rifled muskets; the 1873 Trapdoor Springfield. In bringing out the rifle, in Feb. 1873, the War Dept. admitted that eventually actual repeating rifles, magazine weapons, would be needed. But it did not say when.

Over the next 12 years, the Armory would make improvements to the Trapdoor- make an extractor that didn't shred cartridge cases quite as often, make parts of steel instead of iron, add an adjustable sight. And the Army would test magazine rifles, like the Lee, the Hotchkiss...but in 1885 the War Dept. said, again, that though it knew repeating rifles were going to be a thing of the future, "there was general satisfaction" with the Trapdoor in the Army and no reason to change.

Why? At least some of it was likely sentimental. All the officers who were now in charge of the War Dept had once drilled and fought with the rifled musket, and the Trapdoor looked like one. It was long, it had barrel bands, it had a big side lock and hammer to pull back, its bayonet looked like a musket bayonet. A regiment marching on parade with Trapdoor rifles looked a lot like a regiment with Model 1864 rifled muskets. But there was also the simple fact that the US faced no big external threat. There was no threat of invasion by Mexico or Canada, and no interest in colonial ventures ( yet). The Custer massacre was big news, but it was an anomaly: the Western tribes would never actually threaten the existence of the US the way that, say, Prussia threatened France. And, without an external threat, why spend the money? And, the Armory would say, make all new jigs, gauges and fixtures and disrupt all our careful production routines?

This lack of interest was a problem later. When the Armory took on building the Krag rifle in 1890, it had to add another building to its plant. It didn't have anyone in-house who knew about heat-treating steel ( it didn't need to use anything hard for the low-pressure Trapdoor) and had to go find someone to tell them what to do. It did, however, benefit from having watched on the sidelines as the Europeans had solved other problems- had established the superiority of some bolt-action designs over others, worked out box magazines, and figured how to make and use smokeless-powder ammunition. So, although in some ways the US was behind, in other ways you could say it simply was being thrifty.

TL:DR, without a prospect of a major war, the Trapdoor wasn't something that was broken that had to be fixed. And it wasn't.

Claude Fuller The Breechloader in the Service