Well, "couldn't shoot," seems to be stretching the point a bit, but yeah, if your action is long enough why on earth go with a shorter round that has to squeeze itself to perform? I think a 350g @2400fps is a great idea for most hunting, but it seems most 416 owners are looking for just a bit more. There are those who claim 2400 with the 400g, but I'm sure they are above SAAMI specs.
If your action is only 3.34" and you want to keep it that way, then there's still the same reason for the 416-338 as there ever was. And if the 338, 375 C-T, and 458 Win are good (and they are just dandy for what they do) then why not the 416?
HOWEVER... if I had a standard-length action and wanted a 416, I'd have a hard time not going with the 416 Howell. Or something like it, say a 416-375 Dakota. It will definitely ride side-by-side with the Remington at similar pressures. Brass is more expensive, but not prohibitively, and if you lay in a stash of 200 cases then you're set for the life of the gun most likely.

If youre making a rifle just for Africa, i'm a lot agree with the others here.
BUT if you want a hard hitting, large-hole-maker, for moose or something like that I'll surely recomend the 416 T.

I've used it for moose a couple of years now, and have killed 7-8 moose with it, and I love this rifle. This one I'll newer sell. This is my No.1 mooserifle!!

Have really good results with 340 grs. PP-bullets from Woodleigh. I use low velocity (Approx. 2330f/s), and the meat ain't bad at all.
On heavier, and dangerous game, I'll recommend to increse the loads and maybe go for a 400 grainer.