It's to try and make the brand as ubiquitous as, say, Coca-Cola. They don't have problems selling Coca-Cola as such in South Africa or Kenya. But the nationality-based airline system, and the system of bilateral air services agreements, means that British Airways can't operate domestic routes within South Africa or regional routes from South Africa to nearby countries without using the medium of a South African (or other regional) company.
Franchising is really the only way of making sure that there is a "British Airways" branded flight between Joburg and, say, Durban. If they didn't franchise, then the passenger's "British Airways" experience would have to stop when they walk off the mainline aircraft in Joburg and walk on to some other carrier's aircraft. This way, they can continue to fly "British Airways", and get what they expect from that brand, all the way to Durban. (In fact, they usually get a bit more on that flight than they'd get from a comparable short-haul on BA mainline within Europe, but that's another issue altogether.)