It's all so situational. Maybe you're after buffalo and get in a solid hit but, for extra insurance, use the second barrel as he turns to go away. Is it needed? If the first shot was good, no. It's all part of the romance of the hunt, in Africa, carrying a double. However, many of us simply cannot afford such an arm (at least not one worth owning). So, if you want to shoot a large, historic caliber such as a 470 your only other option is a decent single-loader. A good falling block can be had for much less money than a quality double and, really, is no less romantic, the design having its own, storied history on the African continent.
In essence, no client is in the same position as those of the past, the hunters whose tales we love to read (Selous, Stigand, Bell, Sutherland, Taylor), and therefore the need to carry a double (not that Bell ever really did...nor Stigand, for that matter) simply does not exist. We're all backed by a licensed PH who is there to prevent a sticky situation from occurring (and, there to sort the mess should things go south). So, we don't need a double. Nor do we need a bolt action (I've watched enough videos to know that 99% of hunters do not properly manage their bolt rifle anyway). The best thing the client can do, in my opinion, is bring a scope sighted rifle (bolt, single, or even double (which, I admit, is pure sacrilege)) which he/she can (and does) shoot often. The placement will be more certain and therefore the outcome better for all.