A New York Times article a few years back tried to find out why health insurance companies didn't cover the cost of test strips for diabetics who needed to check their blood sugar levels. Test strips are fairly cheap, and without them, it's impossible to control one's blood sugar. Uncontrolled diabetes can eventually lead to lots of bad medical problems, like kidney failure, limb amputation, and cardiovascular disease, all of which are quite expensive. Wouldn't it be profitable for insurance companies to cover test strips now and avoid complications later?
The answer the Times found was a cynical but rational one. People spend an average of something like seven years with their health insurance company before switching to another (perhaps by changing jobs, or by their employer changing health insurers). If one insurance company provided test strips free of charge, the savings in eventual health costs would be passed on to that company's competitors. When insurance companies emphasize prevention, they lose money.
For years I've had an idea that I've never seen anyone suggest. What if your health insurance company also provided your life insurance? That way, there would be some added profit incentive for your insurance company to keep you alive for longer.