National Fire Administration Statistics

The last set of statistics from the US Fire Administration web site is from the year 2005.

Since the types of fires are grouped using broad terms, electrical space heater fires are lumped in with all other "Heater" fires. Still, I'm willing to bet the vast majority are electrical space heater fires. We hear the news stories all too frequently.

Property Loss
There was $6.8 Billion property loss in home fires. Only half those fires had known causes. 14.3% were determined to have been caused by heating, faulty wiring, cords and appliances. That is almost a billion in property loss for the year from those causes. LINK.
Totals add up to less than 50% because half all fires investigations resulted in "undetermined" cause. So the SmokeShutoff would actually have addressed quite a bit more.

Deaths
The US Fire Administration recorded 3055 fire deaths in 2005. Only 42% of those fire deaths had a recorded cause of fire. 207 deaths were attributed that year to heating, electrical distribution, and appliances. Many of those could have been prevented by shutting off power at the first sign of smoke.

When we look at fires caused by children, cooking, or undetermined causes, there's a likelihood many of those deaths also could have been prevented by the Smoke Shutoff.