Ya don't run them that fast. 180-220gr at 2400 fps is plenty.
Winchester was the first major firearms manufacturer to offer these cartridges to the general public in a quality rifle at affordable prices, and Western Cartridge Co. simultaneously began offering a number of loadings for the .300 H&H—loads that were eventually some 200 fps faster than the British ammunition. Originally, velocities for 150-, 180-, and 200-grain bullets were on the anemic side, listed as 3,000, 2,700, and 2,350 fps, respectively.
There's less effort to seal the case mouth, and extraction and resizing is a breeze.
"...And there came a voice to him, Rise, Peter; kill, and eat." Acts 10:13