My friend was an Air Force accident investigator who strictly investigated USAF accidents and foreign accidents involving fighter aircraft we had sold to somebody. In these particular brand of accidents, fire was rarely the cause of death. Fighter aircraft, of course, have much smaller cabins and fresh air is a canopy jettison away. In a lot of his crashes, the primary cause was either a bad batch of fuel or they simply ran out of gas. Also, if you consider that a lot of pilots can simply punch out of military aircraft, especially ones on fire, this reduces the number of military aircrews who survive a crash where the airplane was on fire at impact. In a lot of his crashes, the airplane bounced first, which can cause a fire, and became airborne again for about a half mile or so. In this case, it's debatable whether or not the pilot was killed by the first, second, or third impact. They would often arrive at the crash site and walk in the direction of flight to find the first indication of impact -- usually broken tree tops or a scuff in the ground.

I definitely agree, for survivable commercial and general aviation crashes, that smoke inhalation is a more likely cause of death.