I can't see any reason to hunt with a double except for the "cool" factor. I've been on three safaris, all with a bolt action. A couple of experiences come to mind.
My first elephant took off running at the shot, as they tend to do except for a brain shot. I got in two more shots before it disappeared. Were all three necessary? I dunno. Could I have done that with a double rifle? No.
My second buff fell down at the first shot. Although I didn't know it, it's spine was broken. What I did know was that it kept its head up, so I kept shooting. Four shots total and all hit. That would have taken longer with a double.
Once when tracking a buff herd, we came across a good zebra, which I shot with my .375. The range was a bit beyond what I might have attempted with a double.
So it goes. I disagree with those who say you can get a third or fourth shot off as fast with a double as a bolt. Under carefully set up conditions, some can no doubt do it. But who is going to hunt all day with two extra cartridges stuck between the fingers of their left hand, or whatever? To say nothing of dropping them in the mud under the pressure of a fast reload. In the real world a bolt action is faster. I even think it's almost as fast for the second shot if you know how to work the bolt while the rifle is recoiling (most people don't).
I am a Sporting Clays shooter and realize that, with my shotgun, I can fire the second shot a lot faster. But 12 gauge target loads do not recoil as much as a .470 Nitro Express, and I'm not trying to hit the CNS. In fact, most good shotgunners don't even look at the bead, but just the target. I don't think you can do that with a rifle. As for looking at rifle sights, target acquisition is a lot faster with a scope than with iron sights, no matter how good your vision is.
