What's the differnce that made rifles so prominent over swords, why use them more in the 1800s than the 1600s or the 1700s ? The first rifle to fire more than a single shot before reloading was made during the First World War, so it couldn't have been the fact that Rifles shot more bullets or something, and even during Napoleon's era, the rifles took 17 or 16 steps to reload!
There are several errors in the technical summary you give.
First, line units did not generally use rifles prior to the mid 19th century, replacing smooth-bore muskets. This allowed for an increase in accuracy at range. This was followed by the development of breech loading, bullets that were lighter and pointed, and smokeless powder. These developments (and others) revolutionised firearm capabilities leading up to the 1890s. Accuracy, range and rate of fire were greatly improved, in addition to the fact that firing in lines no longer obscured the shooter's vision. Under these circumstances, closing the gap between firing and melee range became incredibly dangerous.
Point of order, the first military rifle with stored cartridges was the Winchester Model 1866, famously employed by the Ottoman army at the siege of Pleven. Every major power in WWI had adopted a stored cartridge rifle as its main weapon prior to the conflict, with capacities ranging from 5 (Mauser 1898) to 10 (Lee-Enfield) cartridges.