To me a handgun is convenient and/or concealable. It what I carry if I might need a gun but carrying a rifle is not appropriate. If I'm carrying a rifle, I don't bother carrying a handgun. I can't imagine me noticing something or someone dangerous before such a time that it/he has gotten so close that I cannot deploy by rifle but could still deploy my handgun.
That said, I could see it happening if following a wounded leopard where it could get on top of you before you knew what was happening and a handgun could be helpful. Unlikely enough scenario that I'll not put too much worry into it. Or as above, for finishing hogs if you are doing a volume shoot and might have a number of wounded that you'd rather shoot with a cheap 22 round than a rifle round. Perhaps as a PH or guide who is usually carrying a rifle but has situations where he needs his hands and access to a weapon at the same time, it may make sense to just keep a handgun on rather than only put it on when he puts his rifle down. But for regular hunt, I see no need.