Hum, cartridges we should get rid of?? Well that sounds un-constitutional to me. But I may as well add my nickels worth to this.
1) All rimfires, if you can't reload it you've lost about 90% of the fun in my book.
2) Not much point in anything smaller than a 6mm bore diameter.
3) In the 6mm/.243 bore we need about 3 cartridges:
a) a small case holding maybe 20 grains of powder at the most. That would make a fine small game cartridge. With just a bit more umph than the Hornet. Great for the 60 and 75 grain bullets.
b) a medium case, 30 to 35 grains of powder, like the 6mm PPC for the bench rest crowd.
c) a small rocket with about 50 grains of powder capacity i.e. the .243 Win, not enough is gained by going larger to really make a difference.
4) The .257 bores and the .264 bores are so close together that we should just pick one. Me I'd go with a 260 Rem and that would be the end of the story.
5) The .277 and .284 bores have the same problem, so bye bye to the short list of 270's. Now we've gotten up to a bore that can handle some more powder capacity. Anything that will throw it's midweight bullets faster than 3000 fps is a complete waste of time. Don't want to have performance problems at 50 feet from bullet failure. Breaking that speed limit is loud, has too much muzzle blast, more recoil than necessary and is hard on barrels to boot. So I'd grant the 280 Remington as the only 7mm of any real utility.
6) Thirty caliber well I'd grant survival to the 308 Winchester and the 30-06. If you need the energy of a 300 Magnum you really just need a bigger bullet.
7) 8mm including the 325 WSM really do the same job as the 30-06, don't need 'um.

338 bore, now things are starting to get interesting. For the light end, the new 338 Federal is the weak sister of the MAGNIFICENT 358 Winchester and may even be a commercial sucsess story. Then there is the wonderful 340 Weatherby. Leave out the 338 Winchester, why stop there when the 340 is a real BIG game rifle for the bullets of 250 grains on up.
9) We are approaching heaven now. The AMAZING 358 Winchester will drive a 250 grain slug at 2400 fps for 92% of the energy of the GRAND 35 Whelen using 15% less powder. The 358 Win with 150 to 180 grain 357 pistol bullets makes a grand varmint rifle. The 150 grain slugs can even break the 3000 fps barrier if desired. The 180 Hornady designed for Single Shot Pistols is spectacular for Coyotes and is designed to operate in the 2200 to 2300 fps range. This load is also the funnest plinker for pop cans and milk jugs ever thought of. The 200 grain spitzers can be pushed in the 2700 fps to 2800 fps range. At these speeds comparing a 7mm Rem Mag with a 150 grain at 3200 fps and with both rifles zeroed at 200 yards, the drop is 6 inches for the 7mm and 9 inches for the 358. In feild terms that small gain in trajectory for the 7mm Mag is paid for with much worse recoil, muzzle blast, noise and a larger heavier rifle to boot. The 225 grain bullets will go 2550 to 2600 with great trajectory. The 250 grain at 2400 only drop 10.5 inches at 300 yards when zeroed at 200. This is a wonderful ticket for Elk and Moose. If one desires to go after BIG bears the 280 grain Swift and the 310 grain Woodleighs are just the ticket. Although for this job I'd really rather go with either the 35 Whelen or the 358 Shooting Times Alaskan, which is the 340 Weatherby on steriods. So I'd grant the 35 bore 3 cartridges 358 Winchester, 35 Whelen, and 358 ST Alaskan.
10) 9.3mm X 62mm is amazingly efficient (366 bore) and might even allow the 57mm length also as it is a bigger, heavier version of the 358 Winchester. Same ballistics with a 286 grain as the 358 Winchester with a 250 grain.
11) Well I'm sure by now you're thinking he's got to include the grand old 375 H&H. But in this bore there are two I like better: the 376 Steyr which is a lengthened 284 Winchester case with a full size 0.50 rim and base and the 0.475 shoulder. Case length on this one is 2.36 and case capacity is a bit over 60 grains. This one drives the 300 grain bullets at just over 2400 fps which is optimal for maximum penetration. The other .375 is the .375/325 WSM which is ballistic twin of the 375 H&H in a short action rifle.
12) Time to wrap up. The last two are the 416 Taylor, which is the 458 Winchester case necked down to 416. Which is very close in performance to the 416 Remington with less powder burned. Finally the 458 Lott which overcomes the weaknesses of the 458 Winchester. The 458 Win usually chronographs at about 2050 fps, while the Lott gets an honest 2300 fps with the 500 grain bullets.
So now that we have our list of keepers, we can just throw all the rest out. If you want or need to live with only one rifle, get a Browning BLR in 358 Winchester and you are set for everything in the world. The 310 Woodleigh Solid has even taken Elephant and Cape Buffalo.