Monitored policies are almost always significantly cheaper. That's why people buy them. I won't engage on who the "idiot" is in that analysis except to say that Adam Smith probably has an opinion.

The reason this works is that it forces the consumers to self-partition into those who think they drive safely and those who know they don't. That doesn't correlate perfectly with actual safety, but it's clear that it's a good proxy signal. Insurance companies may be renowned for "slippery policy wordings", but they're even better known for doing good statistics.