Miss the brain with a .416 and one gets the same result. One has to get much heavier than a forty for KO to be a consideration on dangerous game if the shot misses what matters.
I also think your .410 analogy is wrong. It truly is a gun for experts when used on game like quail. However, the .375 will do anything a .40 will do if a premium 300 gr bullet is placed in exactly the same place - solid or SP. I know that is annoying to the forty owners (I would add that I own a .470, .404, and 500/416). Unlike a .410 in an inexperienced wing shooter's hands, the .375 is ideal for the client transitioning from his scoped deer rifle to something that will cleanly kill a buffalo or an elephant.
If you want to use a shotgun analogy, I would say that the .375 is more like a 1 ounce load from a 12 bore when used on upland game. The short shot string makes it just as effective for everything but waterfowl as a heavier load but in most shotgun configurations is far easier to use effectively. I should note that I base that on thousands of pheasants taken with an ounce of No. 6 shot.