Let's say we (as a country) ban life insurance and health insurance as separate packages  and require them to be combined in something I'll call "Longevity Insurance". The idea is that as a person/consumer, you can buy a "life expectancy" of 75 years, or 90 years, or whatever. In addition, you specify a maximum dollar amount that the longevity insurance will ever pay out--say, $2 million. If you have any medical issues throughout your life, up to the life expectancy threshold, the insurance plan will pay for your expenses. If it fails to keep you consciously alive for the duration of your "life expectancy", then upon your death, the policy guarantees that the company will pay the full remaining amount to your next of kin.
It seems like this arrangement would put all of the right incentives  in place for both companies and individuals. Most individuals would want to avoid trivial medical expenses in order to maximize payout to family in case of accidental death. Companies would want to maximize health and longevity in order to profit from the end-of-life payout. And our society would have a way to rationally consider the value of life without resorting to arguments that essentially conclude "life is of infinite value," and in doing so, prevent sensible gerontological triage. To put it into perspective, it makes little sense that we spend $1M (as a society) trying to save a 92-year-old when that same amount could have saved 10 teenagers.
Longevity Insurance companies would be incentivized to become heavily involved in medical research that prevents disease, prolongs life, and keeps people healthy. I can imagine a whole array of things that make sense in this context. For example, it would be the right place to fund studies on genetics, it could be the right vehicle for getting 'free' immunizations, and it could even make public funding for "health insurance" easier to pass--simply set the bar low enough that everyone can agree on an age that society will extend a policy for. Do we all agree that everyone in our society should live to age 50? Super! The government will cover Longevity Insurance up to age 50.
 We could also just allow Longevity Insurance as a free-market alternative, but for the sake of argument, let's ban its competitors.
 The one incentive that Longevity Insurance does not seem to address well is the possibility of next-of-kin killing their loved one just prior to the end of an insurance policy. One option would be to require a one-year moratorium in the case where someone dies within a year of their policy ending. This would give time for an investigation before awarding large sums of money.
* crosspost from my blog, http://halfcupofsugar.com/longevity-insurance