Also, IIRC (see above at "dotage"), US infantry in the Spanish American war were still carrying black powder trap doors. Cavalry, Rough Riders and Buffalo Soldiers, were armed with new, smokeless, 30-40 Krags at Kettle/San Juan hill.
Oh, and Gatling Guns.
The SMLE lost its magazine cutoff (along with a bunch of other outdated features like “volley sights”) in 1916. I think the model was the No. 1 Mk III*.
Back home in the States, 1903 Springfield rifles continued to sport a cutoff right to the end of production in 1944-45.