A genie has granted your wish to be able to name three new cartridges to be in the stores for you and the public. However you must obsolete two old ones for each new one.....
The 338-06 is already comercially loaded and chambered. Be it only Weatherby but it is a comercial cartridge.
My list would be...................
358 ultra mag
270-284
338-284
You could get rid of every single belted cartridge below .375" bullet diameter.
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First of all, you can't get rid of the classics like 25-06 and 30-30 Win. Also, dumping all belted cartridges under .375 inch diameter would mean an end to the 7mm Rem Mag, 7mm STW, and a bunch of the Weatherby's...you can't do that either!
IMO, you can get rid of all but the best round in each cartridge class, with a few exceptions. This is what I would keep (rifle cartridges): 22LR, 223, 22-250, 243, 25-06, 257 WBY, 260, 270, 7-08, 7 rem mag, 7 STW,30-30, 308, 30-06, and for 338 and up, I don't have an opinion. Anything.30 cal and smallernot on this list could be dropped...although, maybe the 257 Roberts and 6mm Rem could stay as well.