How frequent are such situations? With safety stuff you always have to weigh lives saved when the safety measure works as intended against lives lost when it doesn't.
E.g., seatbelts save about 15000 lives a year in the US. But occasionally someone is killed who would not have been killed if they hadn't been wearing a seatbelt, like this guy [1] whose neck was fatally compressed by his seatbelt. Politifact had occasion to look into deaths due to seatbelts [2] and found them rare, and worked out that if every crash that ended up with the vehicle on fire or in water with the occupants wearing seat belts ended up killing them it would be a couple hundred or so per year. The real number is going to be much lower than that.
I can't find any statistics on pyroclastic flow in the US, but in the last 100 years it looks like there have been under 100 deaths from volcanoes, which should be a superset of pyroclastic flow deaths.
How many more would there have been if those who avoided being one of those 100 by fleeing in their cars had cars equipped with the new system? I'm guessing that it would be less than 10x as many, since it is mostly only going to people who stuck around long past when evacuation was called for. So 10 per year.
As a check on that, I've seen estimates that over the last 2000 years in North America there were around 5000 deaths from volcano, so on average less than 3 per year. Since most of those were at times when people didn't have cars, volcanology was much less advanced, and communication was much slows that number should be higher than what we'd have nowadays even if cars were very flakey when fleeing from volcanoes. This suggests that my guess of 10x is very generous.
Drunk driving kills about 10000 per year in the US, so to make a persuasive argument based on deaths from false positives you are going to need much more than increased pyroclastic flow deaths.
Someone has brought up driving erratically while rushing to the hospital to give birth. I haven't found any stats on that. I'd guess that it is not super uncommon, but also that most of the time if you don't make it to the hospital in time it is not fatal. (And also increased deaths due accidents causes by rushing to the hospital should be considered...).
Anyone have other ideas? If the anti-drunk driving technology only prevents a quarter of drunk driving deaths that would 2500 per year, so we probably need at least 50 to 100 deaths per year due to false positives for that to be an effective argument.
[1] https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4608342/
[2] https://www.politifact.com/factchecks/2011/jul/13/joseph-tri...