The advent of rimless cartridge made all this redundant.
Remember there are two kinds of designs (for everything).
One kind is a design that is new, original and never done before.
The other kind is a design intended to "work with what you've got..."
And, what America had in the 1890s was rimmed rifle rounds. Looking at "modern" military rounds (meaning designed/readily adapted to use cordite or smokeless powder) The start is about 1888, in Europe. The French 8mm Lebel, and the British .303, both rimmed, and the German 8x57mm Mauser, which was rimless. The .30-40 Krag arrives in US service about 1892, the same year Mauser creates the 7x57mm. Other rounds show up in the later 1890s in Europe, remember all these are within a few years of each other.
The Spanish-American war was the first conflict of significant size where the advantages and disadvantages of cartridge and rifle design in combat were a significant lesson. Rimmed vs rimless, and Krag vs Mauser box/stripper clips.
Rimmed vs rimless was not a clear cut lesson for everyone at the time, or for some time to come. Krag vs Mauser box/stripper clips, was.
Britain and Russia/USSR kept their rimmed round, The US went rimless. Adopting many Mauser ideas into the 1903 rifle and cartridge.
Here's an interesting tidbit, the Krag system also works fine with rimless rounds. I have a Norwegian Krag in 6.5x55mm. Made in 1897. The Krag design was not limited to rimmed rounds, it just worked with them and that't what America used in them. Other nations used their own (rimless) cartridges in their Krags.
So, if someone tells you that the Krag was pulled from US service due to the "obsolete" rimmed round used, they're mistaken.
The Krag was replaced because real combat experience showed it to be inferior to the Mauser system's firepower. I know of no reports about the Krag's slower reloading speed vs the Mauser from the Philippine insurrection. Probably due to the fact that the Moros weren't armed as units with modern Mauser rifles.
The Krag is a great system and has a certain kind of elegance to it. It was surpassed by a design was superior in infantry combat, because the Mauser reloaded faster, but that's about it.
Note that the British kept a stripper clip charged 10 shot rifle with a rimmed cartridge the Russians a 5 shot one, and the rest of the world pretty much went to 5 shot magazine rifles using rimless cartridges., and this situation lasted pretty much until or through WWII depending on which nation you're looking at. The US was a little ahead of the curve with the M1 Garand, and after WWII every major nation replaced their bolt guns as the primary infantry arm within a few years.