I’m slowly going towards exactly that. One rifle, one scope, one chassis, several barrels with some shot more often than others. Probably shoot 6.5CM in the summer and switch to .223 in the winter (don’t feel like hiking more than 600m in the snow to place targets).
I went this way awhile ago although I don't sell fur so if I did I'd probably have a dedicated coyote rig. I took the love child of the 6.5CM and the .223 and just built around it. The 6.5 Grendel (introduced 2004), the 6.5CM (introduced in 2008) so the Grendel was actually here first. Sure the 6.5CM burns 43 grains of powder and the .223 somewhere around mid 20 grains would be my guess. The 6.5 Grendel burns 30 and loves the 123gr bullets. We've got 8 head of big game now, average shot distance 170 yards with average recovery distance of 10 yards, coyotes don't like em either, have at least 4 of them as well. We've got moose, sheep, both deer and black bear so far, zero issues, a joy to shoot and does it all. A 21st century 30-30 is what the Grendel is. The two most efficient users of powder going are the 6.5CM and 6.5G, one could think of the 6.5G as the 6.5CM Short.

No switch barrels needed, can kill 3rd class game to 400 yards, deer as far as you might try. My 16" barrel 6.5G still has 1800 fps to just over 400 yards with 123gr Hornady Factory ammo, a 24" barrel would be 520 yards (15 yards per inch of barrel length gain fyi). Since our hunting will be exclusively under 400 for big game and can still dial up coyotes as far as we like...the 6.5CM was just a little overkill haha. 4 seasons (fourth not quite done yet, looking for a doe or two this weekend) and we are very happy with what we've done with the 6.5G in Alberta.
The 6.5CM gets my nod as the most efficient period as it can stretch its legs a couple hundred yards further with a higher SD/BC bullet to boot. 600 yards is nothing for it and the bullets are well up in the SD range for class 3 game work. We don't care much about trophies and have no problem working our way closer but we predator call plenty in winter although not to sell hides so we've found our blend in one cartridge with the 6.5G.
Other things I like about 6.5G is 52,000 psi cartridge, barrel life should be limitless in bolt action rifles and ammo affordable. Also anyone shoots it well, so put in chassis with adjustable lop has been fantastic for the kids, the Ruger allows 10 round mags as well so that's a bonus (AR Pistol Mags). Rifle choices a bit limited however being AR length cartridge, CZ, Ruger, Howa...I've built them all up and prefer the Ruger American platform as the no gunsmith working man option, holds 3/4 moa for me out to 500 with Hornady factory ammo for 3 shot groups.