It's just as easy to mess up the second shot as it was to mess up the first shot which resulted in the charge. Actually, given the added stress of trying to clean up the mess while the animal is on its way to kill the shooter, I would safely estimate it's a LOT easier to miss the second shot. Then what? Trying to reload a break open gun on the run. How's that gonna work?
The idea of hunting dangerous game with a PH or guide is to employ the "platoon effect" in the event of a combat situation. The team protects each other firing in volley. In theory the client takes the first shot. If the animal charges, the PH should be ready to followup immediately. And if his shot doesn't stop the animal, then the client should by then be ready to fire again. Or an additional PH or client. However, I have seen many videos of either or both client and PH haphazardly firing both barrels so fast that followup shots were badly placed or missed altogether.
We are drifting to the same old worn out topic of bolt vs Elmer Fudd double gun. To return to the original theme, I don't see much attraction for either high end bolt or low end double, but certainly, if I was prone to excess, I would choose the former because it is more utilitarian and, in my view, the safer choice. I choose to drive a 2004 Envoy rather than a new Corvette convertible. Both will get me from point A to point B but in the event I'm met by a charging Jeep that crosses the centerline, the former probably has a better chance of keeping me alive. For sure, no one will turn their head watching me drive by but how important is that? And the Envoy has the added advantage of cargo space for my dogs and being able to egress without employing a shoehorn.

. It's all about what turns your crank and I appreciate those who admit whim or nostalgia are the reasons for their choice. Those who try to argue an ultra expensive double rifle is the safer choice ... sorry. I'm not buying that.