Well… an oil painter would not add black. Rather they would add the complementary color. This would darken and also neutralize the base color. A digital painter

Well… an oil painter would not add black. Rather they would add the complementary color. This would darken and also neutralize the base color. A digital painter could achieve the same effect with a simple multiplication (add black via multiplication blend mode). As you imply, the outcome is not always realistic. The reason is that the shadow would be tinted by the environment light. This is particularly apparent in desert environments or very sunny environments where the shadows can be a saturated blue.