If rifles count, I'd argue that the most successful recent rifle cartridge is the .300 AAC Blackout / .300 Whisper. Another contender is the 6.8 Remington SPC.
That is ironically backwards. The .300 Blackout is just the .300 Whisper of the 1980's, and that was based on the .30/5.56 wildcat that early 3Gun shooters were attempting to introduce as a dodge around rules allowing only .30. The intent was to exclude the M16 as it was in very low regard. Once accepted, tho, it came to dominate the sport for very good reasons.
But the .30/5.56 - .300 Whisper languished for nearly 30 years. In the meantime the 6.8 and 6.5 were separately created, the first by Special Forces and the AMU, the second as a long range precision shooting wildcat adopted by Alexander Arms and re-engineered. If anything, the first is just a .30 Remington necked down to .270, the second the 7.62x39 necked down to .264.
AAC picked up the .300 Whisper ten years after both had been introduced and established on the market. They are both much more successful as barrels, bolts, and ammo are widely available, and both are highly popular with hunters and shooters who go after live game.
The .300 BO isn't considered a good long distance round, with similar ballistics to the .30-30 or 7.62x39 because it begins losing a lot of velocity and dropping. Not too many talk about it for hunting use, what does come up is building pistols with wrist braces for PDW use or suppressed at close range, it's actual intended purpose by AAC. And that means adding an $800 surcharge for the suppressor.
While it may be inexpensive to assemble and lots of threads talk about building one, there is very little traffic yet about using them in the field. It's a range toy, not much considered for actual hunting and defense when the other two cartridges have been selling purpose built rifles for a decade already.
The .300BO also has to compete against it's origins - and there are those who hunt with 5.56 out to 400m, whereas the .300BO is limited to 250. While it may be a topic of hot interest at the moment, overall, the history as a wildcat is old, extensive, and marked with a lot of disinterest by the general public and those who would have used it in the AR if it was any good. The 5.56 in cheap military surplus does their job better.
There is the largest obstacle with bringing out a new cartridge these days, the middle ground is pretty full of existing and well rounded ones that pretty much fit all the normal working niches. What we see in the lists above are at the extremes, or for unusual purposes, either magnums or sub -.22's, suppressed or limited range. A newer cartridge has to actually do something better - like have 50% more power than the traditional round in the same gun, or double the effective range.
Being a cheap wildcat doesn't make it a great cartridge, which is why so many fall by the wayside and stop being produced.