First, the .300 Weatherby has committed the cardinal sin of becoming old. Introduced in 1944, commercial ammo was first available in 1948, which makes it either 63 or 59. Some cartridges, like the .45/70, are so old that they become trendy by dint of their sheer age. The .300, however, falls into that netherworld where it is Old News.
Second, as an all-around rifle, it is not a particularly good choice for the average shooter because it is a handful. Recoil is not particularly awful, but the noise and muzzle blast are considerable, and it’s a lot more than many people can handle.
Third, for a truly all-around rifle, it lacks bullet weight (this is said with the knowledge that it has killed everything on earth, and I do mean everything, many, many times over); for an all-around rifle I’d rather have its larger brother, the .340 Weatherby.
This said, I like it so much that I own three .300 Weatherbys, the only rifle that I own three of. It is a highly specialized long-range load for genuinely big game, and as that, it has few peers and no betters.