Problem is that you would have to do the logging in a very uneconomic way.

Basically you would want to leave the most profitable trees (big/old ones) and cut down all the small ones. This is because big trees don't really burn down and survive the fires for the most part. After a fire they provide a canopy stopping the forest from growing to be as dense in the future. With the less dense forest the fires after that won't be as intense.