The chances of an ember taking off and flying into dry brush is non-existent with a camp stove. The chance of one, even with a small fire, is far greater when burning wood. That is not to say that one cannot start a fire with a camp stove, but the odds are far less. Of course, there are also the other numerous issues others have listed: firewood collection, "leave no trace", etc. FWIW, the northern two-thirds of Michigan is currently under "High" or "Very High" fire danger.

That said, I cook directly on fires frequently, whilst in a campground with established pits. I've got a cast iron frying pan and kettle I stick right in the embers. Nothing better than some bacon and eggs fried in the grease from a cast iron pan on a campfire in the morning!