I'm no ballistician. I've seen photos of .300 BLK being used to absolutely destroy hogs and coyotes with no issue. But I'd say it's very, very light for elk except at shorter ranges. A coworker, who when he's not hunting bad guys is a professional hunting guide, doesn't allow any of his customers to use less than .30-06 on elk, preferably heavier.
Not necessarily because elk are bulletproof, but he's seen guys make bad shots or bullets just not perform and he's not willing to risk losing the animal on an iffy shot. Anything up to non-Iowa-huge deer, it's probably going to do fine, but an elk is a big damned animal at any range. I know people who've gotten the job done with a .44 (close range) and various other rounds at intermediate distances (200m). I just don't think i'd personally use the .300 for that. I know Mark LaRue dropped an elk at 400m with a 6.5 Grendel (and a couple .308s a few years later) but that was with laser ranging, perfect shot placement and perfect bullet performance. I used my 7x57mm Mauser, a century old, to drop a red deer (250-300lb) with a single hit at about 65m, the standard softpoint more or less vaporized the deer (both lungs and a spinal hit with 1 shot) and it was DRT. That's a 173 grain round, fat and medium velocity. It'd probably "do" on elk (the 7mm has killed just about everything in Africa of similar size) but I don't know how well the .300 bullets are constructed ie would they blow up on impact or hold together and get the penetration really needed.