While ahead of the .375H&H ballistics in thumping game, the .40's are still hunting rifles, just as the .375 is a 'legal' hunting rifle. They are 'all round' hunting rifles for Africa. but big dangerous game and plains game alike. They need to be fed ammo that shoots alike, but covers the requisite duties.
Stoppers?, no - they are hunting rifles and as such, are easier to hit accurately with and thus, with perfect shot placement, they should never have to be used as stoppers.

After all, that is what the PH is for, is it not - in an emergency situation, he sorts out the trouble with the stopping calibre.

Do YOUR stuff, learn your gun and hit correctly - that is all you have to do and a hunting rifle is what is best for that game, not a stopping rifle. imho of course.

Buddy of mine is headed to Africa soon, and will be packing his .375 Ruger or .375H&H, not sure which, along with likely his favourite 8x68S. His wife will likely pack her new favourite, a .270 with TTSX loads.

He is deadly accurate with both & long range is not a negative factor with either- he's the best game shot I have ever seen. She shoots very well too - last elk over 400yards, one shot DRT & she has an excellent coach.

If he uses more than one shot per any animal, it will only be because the PH asks him to shoot again.