That's a very good point. Maybe some people would pay a little extra for a health and safety service package that covers all your needs, not just the unusual events.
Current insurance companies not incentivizing and helping their customers achieve a healthier and safer lifestyle is absolutely an indication of how far the system is from a free market and how much we need something better.
For example, in Finland we have a public health system funded by the taxpayer, which effectively subsidizes junk food, tobacco and other harmful products that would be less popular if you had to pay higher premiums.