I guess it depends what the "it" is that you want them to do.
I have friends who hunt with both the 404 and 416 and they could have chosen anything. The are very happy. At big bore shoots both calibers feature strongly, so they are certainly popular amongst sport hunters.
The guy with the 416 was a PH in Tanzania for a couple of seasons. There is also a very senior ranger in the KNP who currently uses a 416 (unless he has his new rifle already). He tested it extensively against other calibers in both the field and in inanimate penetration tests and believes it is the king of penetration, although he is now building a 450 Rigby. His requirements are obviously different as stopping charges are central to his job and he is often all alone. He has been well served by his 416 though and it is just brute stopping power that has him looking elsewhere. His words to me were that he has never had a problem with his 416, but when you encounter these type of situations often, you never know and one day he may need that "bit more".
As I recall Kai Uwe Denker uses/d a 404 for back up and Tony Sanchez Arino a 416. There are others who used both, but I don't recall who. I know that Taylor recommended a 404 for buffalo in herds - I think he suggested it directly to Brian Marsh.
There are others more qualified than I to comment, but my limited experience is that for back up PH's tend to favour the .45's over the .40's. There are other discussions here on charge stopping requirements and the classic ballistics.
I'd like to ask though, if not these calibers, then which? In other words if they aren't cutting it, what did you think may have replaced them? The .40's you've mentioned don't seem to have much competition in the bore size as an alternative, although the new Ruger may be promising. Most guys I know who tried the 416 Rem moved away from it as they struggled to get the velocities without unpredictable pressures.
I've no direct experience of the 450/400, but it's in the same class.
I think the answer in an unequivocal "YES"!
