We have addressed this in various episodes but to be clear:
Better access to Ottoman accounts (a translation was made available from the Turkish commander) points out the Winchesters weren't used on the line at Plevna. Likely because of limited ammo and lack of range, though to my knowledge there is no reason written.
The Russians likely named them as an excuse for their poor performance at close range, the admittedly bad sighting of the Berdan II was named as the long range problem. That's why all Berdans have updated, longer rear sights.
Regardless, Europe heard the Russian story and, combined with other repeater successes, finally decided to start spending the cash on them. Notably they kept the same service rifle cartridge, which they also struggled to share with any mitrailleuse and early MGs
Single cartridge production also saves on logistics at production btw. Same raw materials, same processed pieces, same training, same inspection, etc. If you have two lines dedicated to rifle and one to carbine running all out for war and you end up with carbine shortages somehow, then you have to have massive down time to convert a rifle line or make new. If all three are the same you just have to worry about global output and not balancing issues.
In wars of attrition small problems start to stack. We all acknowledge Germany suffered from having too many overlapping technologies in WW2, straining their limited resources unnecessarily. The US sat between them and the other Euros, but the US uniquely had an uncontested, massive manufacturing base that allowed for insane wastage without fear.
Even so, the US would need future vision to feel safe using two primary cartridges... and then for what perceivable gain?