Wouldn't it have been more adaptive to develop light skin and so reflect incoming light?
First, I think you have things backwards. Africans came first: lighter skin is an evolutionary adaption to living in more northerly climates.
Second, evolution works with what it has, not necessarily what's best. Mammals had the genes for melanin production long, long before hominids came on the scene, so it's fairly easy to apply selection to increase or decrease melanin production in a population. The classic example is the British peppered moth: https://en.wikipedia.org/wiki/Peppered_moth_evolution (Note: I'm not clear whether the moth pigment is melanin or something else, but the principle holds.)
For a white blocking pigment (or transparent to visible light - think sunscreen) or a reflective skin to be evolved, we'd have to wait around until some mutation happened that would allow the body to produce the right sort of chemical. AFAIK, mammals don't actually produce white pigments: white fur is due to the scattering of light in the absence of pigment. (Just as snow is white.) So animals in sunny climes might evolve white fur, but that makes the animal conspicuous.
Check out this page on skin color adaptation —
Nature has selected for people with darker skin in tropical latitudes, especially in nonforested regions, where ultraviolet radiation from the sun is usually the most intense. Melanin acts as a protective biological shield against ultraviolet radiation. By doing this, it helps to prevent sunburn damage that could result in DNA changes and, subsequently, several kinds of malignant skin cancers.