The 4 bore shotguns like Chuck's were never very common. They were mainly a market hunter's tool used in blinds and boats. Not carried much in the field.
The 4 bore rifles were even less common. They were really more of an evolutionary step in big game rifles as the larger game was encountered by Europeans. You have to remember that VERY few Europeans had been very deep into Africa before the mid 1800's. The Congo was not even established as a Belgian colony till 1890. Those monstrously heavy guns and heavy ammo were not practical for long treks on foot where everything had to be hand carried because the tse-tse killed most beasts of burden.
The 4 bores are really a seldom used approach to the matter. The Black Powder Express rifles came along at about the same time and did an adequate job with far less weight. Baker was one of the first, if not the first, to promote the 577 BPE. It is also known that he had H&H build four 10 bore rifles for his elephant hunting. I think that Baby was not his everyday rifle.

People also realized that the modern bolt guns like mausers would do for the poor man that could not afford the higher grade rifles. John Hunter, as I recall, poached his early elephants with a surplus 8mm Mauser that had a very pitted bore and surplus ball ammo! Being young, dumb, and poor, he just didn't realize it wouldn't work since he was pulling enough dead elephant's teeth to buy fine British doubles in 577 NE.

And then there was Bell, who picked his shots, and killed most of his 1011 elephants with a Rigby 7x57.....