Yeah, cartridges can definitely increase in popularity for awhile after introduction, but today it's tougher than it was when the .338 and .280 were introduced in the 1950's.
In fact the .338 Winchester wasn't all that popular at first, except in Alaska, which I suspect is still the case. It had a little surge here in Montana among some elk hunters, but the big reason it became a factory round was Elmer Keith, who's why Winchester originally offered a 300-grain factory load.
In my experience it hit its peak in Montana a couple decades ago, but the flood of premium bullets made smaller calibers more popular among average hunters--and the .338 Winchester doesn't have enough powder room (or often magazine length) for long-range hunters. It's not dying, especially in Alaska, but isn't as popular as it was a decade or two ago, which is reflected in fewer factory rifles being chambered for the .338.
I found that out while researching an article on how many factoty rifles are chambered for the .375 H&H. In the majority of factory rifles these days, the .300 Winchester is the "biggest" round. The .338 succeeded as much as it has because for years it was the only commonly available "medium" between .30 and .375, but eventually the abundance of premium bullets in smaller calibers ate into its market share.
I dunno if the .280 has ever ever been very popular, and Remington has really tried in some ways, and screwed up in others, such as the dumb-ass "7mm Express" experiment. Jim Carmichel gave it a boost for a while, apparently because he had to promote something other than the .270, but it never was very popular even in the original Remington semiautos and pumps it was designed for, or came anywhere near the .270 in either rifle or ammo sales. Apparently the only people that really care about the .280 are rifle loonies who like to split hairs, but even among long-range hunters it's never led the pack among 7mm rounds.
A bunch of cartridges died quickly even in the 2-3 decades after World War II, when there were a bunch of gaps in factory rounds, mostly because there was no reason for most of them. "New" factory rounds usually succeed because there's some demand for them already. Good examples are the .22-250, .243, .25-06, 7mm Remington Magnum and .300 WSM.
In a way the present "new" cartridge market is a lot like the best-selling book market. In the book biz, if a new book doesn't float higher during the first month after its published, the ad campaign disappears and the publisher puts the money into some book that starts selling better immediately. There's just too little chance that yet another .224 or .30 will last very long, unless it somehow fills a popular new slot, and even then it ain't gonna make money like the .243 Winchester or 7mm Remington Magnum.
