There are a few unstated facts here as well.
The OP is a firefighter. So am I. We work for the fire department. 90% of the job is FIRE PROTECTION. Not FIRE PREVENTION. Prevention is key.
Prevention is eliminating the threat. We cannot eliminate the root cause: People.
What is the next closest step to the idiot with a lint problem? The lint itself.
We cannot eliminate lint, not completely at least.
Then we have the dryer. It does not care what you put in the dryer, but we can regulate it internally. What about the humidistat idea stated before. Sounds good, but I have additional idea. A thermal fuse. If we can stop heat from building up in the dryer, then we PREVENTED a fire. Now we don't need a heat detector to tell us HEY, stupid, the house is on fire, get out.
Now Let's look at the result of a thermal fuse tripping due to improper lint removal. The dryer operator can no longer dry their clothes. They will either call a technician in to repair it, or replace the unit. Either way the fire was prevented.
Let's assume for argument's sake, a repair man was called in. Also let's assume its a decent repair man ( I am not here to debate the efficacy of dryer repair men.)
He will find a blown thermal fuse, determine the cause was the lint. He will then inform the dryer operator, they caused the problem by not cleaning out the lint. FINALLY, we got someone to address the root cause of the problem; The operator.
Now, I do not assume that this will prevent all dryer problems, fuses will not operate properly etc. but it addresses the problem at the ROOT CAUSE.
Also, I hear someone out there saying, but the dryer manufacturer's will balk at it. Sure, but the first one that puts it in will market it as a dryer safer than any other dryer. They would be right, eventually all manufacturers will adopt it to be competitive.
If we add safety features to the dryer, we will not have to rewire our houses. It is a cheaper method and it deals directly with preventing, not putting out fires.