Something else to consider is that charred wood is fire resistant. So after the first cantrip or two, the wood is going to be harder to burn.
In addition, I don't see the whole door going up in flames, I see a fist-sized hole being (very) slowly formed. It would take hours to burn down most doors, and probably create a great deal of smoke. Even creating a bonfire on one side of a door would take a significant amount of time to burn through the door.
It would be an interesting experiment. Take a wooden log (oak or similar hardwood) apply a blow torch to it for a couple of seconds, take the flame away for a few seconds and apply again. Kind of a "spell caster's Myth Busters". Having started my share of fires, if the flame ever did start the door on fire I suspect it would go out in a very short order. You need continual heat for several minutes to get a log burning.
In addition, I don't see the whole door going up in flames, I see a fist-sized hole being (very) slowly formed. It would take hours to burn down most doors, and probably create a great deal of smoke. Even creating a bonfire on one side of a door would take a significant amount of time to burn through the door.
It would be an interesting experiment. Take a wooden log (oak or similar hardwood) apply a blow torch to it for a couple of seconds, take the flame away for a few seconds and apply again. Kind of a "spell caster's Myth Busters". Having started my share of fires, if the flame ever did start the door on fire I suspect it would go out in a very short order. You need continual heat for several minutes to get a log burning.