Why do organic compounds undergo halogenation much more often than inorganic compounds?
Are you sure that they do?
Organic compounds are generally rather inert. It is hard to manipulate an alkane, and often the first step is to introduce a halide by radical halogenation. On the other hand, inorganic compounds TEND to be a bit more reactive, and offer a greater range of oxidation states, which chemistry may allow direct halogenation (without all that tedious mucking about with UV light).