Logging increases fire risk in the short term, because it leaves behind a lot of slash fuels and stimulated brushy undergrowth. It is not analogous to a burn.
Could we place some requirements on the logging companies to leave the ground in a certain state? Or would hauling off the undesirable material make logging unprofitable?
You'd likely run into the same problem of politicians and local companies lobbying against such a rule, in the name of "don't hurt businesses" etc.