"The cartridge is rimmed, tapered, corrosive, erosive, and with a cupro-nickel jacket bullet."
Rimmed. Yep, and it still made a rather distinctive accounting of itself through two World Wars and multiple colonial excursions with remarkably little fuss or trouble, both in bolt and fully automatic weapons.
Tapered. Just about every cartridge is tapered to some degree, even the .30-06. It's the amount of taper that needs to be considered as to whether it becomes a hinderance or not. In a cartridge like the 8mm Lebel, it's a huge hinderance. In the .303, 7.62x54, and rimless cartridges, not such a big deal at all.
Corrosive. EVERY nation used corrosive ammunition as its primary military priming right up through World War II. Some Combloc nations used it long after that. Proper training of soldiers in their cleaning routines obviates that issue.
Erosive. All early smokeless powders were, to one degree or another, erosive. Some of the early American military smokeless powders were like stuffing an Oxy-Acetylene torch down the barrel they burned that hot.
Coupled with the softer steels that were in use at the time, it could be a pretty bad problem, but it was rather quickly addressed with new powder formulations and harder barrel steels. By about 1910 the cordite formulation had been adjusted to the point where it was really no more erosive than any of the other similar powders in use at the time.
cupro-nickel jacket bullet. .30-03 and early .30-06 bullets also used cupro-nickel jacket bullets. I'm not 100% sure, but I believe that the roundnose cupro-nickel jacket was replaced with a spitzer bullet jacketed with gilding metal around 1899. I'll have to check on that when I get home.
In other words, the .303 British cartridge was very similar to virtually all of its contemporaries. While it kept the rim, and the British kept the cartridge, for a number of reasons, none of what you've listed was really a killer issue, and in fact the .303 British gave incredibly good service over its life.
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