When a new cartridge comes out, it’ll be heavily embraced by a small group of customers to whom it’s a real answer they’ve been hoping for, for a specific need or problem. It will also be embraced by another group, who will adopt it because it’s the new hotness of the week, those who must hop on the newest bandwagon or have the latest and greatest. It’ll gather further market share by default from customers new to firearms for whom the new cartridge is the promoted answer to whatever question they’re asking. (“I want to shoot deer at 100 yards” will far more likely end up with a .300Blk or something else new than a .30-30 or .44-40) I submit that a cartridge has to do a pretty thorough job of making converts in all these categories before the average already-committed firearms enthusiast begins to ponder if he needs one in his battery.
What this means in practice is that a new cartridge has the deck stacked against it in the first place, in the quest to become universally popular, and that older cartridges will take a very long time to decline or become obsolescent because their user base, once established, is likely to remain loyal to them for a long time -after all, a gun doesn’t wear out quickly.
So in this light, no, I don’t think new cartridges necessarily “kill” older ones. Some new and old cartridges have a real reason to exist and others don’t, but even the ones that are objectively outmoded will still have followers for a long time. I do think that there are some fine old cartridges that slowly wither (to the detriment of everyone) simply because they aren’t new and exciting. (30-30 is probably losing market share right now, being the primary cartridge of relatively few users now compared to its heyday. On the other hand most of the millions of guns are still around so even if new ones aren’t selling like hotcakes it’ll be a relatively popular cartridge for decades or even centuries. And gun writers have been declaring it obsolete since the ‘20s!) I also think, for a variety of legal, practical, and safety reasons, it’s often easier to create a completely new cartridge than to attempt to breathe new life into an old one. Example: 6.5x55 Swedish. It’s been killing game and performing well at the target range since first adopted in the year 1894. But in the US it’ll never be loaded to its potential in deference to the Norwegian Krags and small-ring military Mausers (many legally antique) which make up the vast majority of weapons chambered for it. It’s much easier to create a cartridge which mimics the performance but with a fresh set of 21st century specs, and no suspect metallurgy, and call it something exciting like …6.5 Creedmoor, or something like that.