For hunting use on varmints and deer-type critters, "barrel burner" is pretty much irrelevant. You just don't shoot all that often. Few of the standard cartridges do any significant burning below some 1,500 rounds or thereabouts. Many do fine to over 3,000 to 5,000.
Two or three deer, an elk, a few coyotes and a dozen hogs, plus maybe a dozen rounds for sight-in? Most any hunting rifle is good for forty years or more. My pet '06 was new back around 1970-ish, and has around 4,000 rounds through it. Still shooting sub-MOA.
So: Coyotes and hogs? I'd prefer a .243 over a .223 for hogs, personally. For coyotes, then, 55-, 70- or 85-grain bullets; 95- or 100-grain for the hogs.
Not saying the .243 is any kind of super-duper critter; I just know that it works. So does other stuff, but I haven't tried a lot of other stuff in my hunting.