From the article:

What we could do instead would be to have health insurance insure health, and in the limit, life. They owe you and your family money if your health fails or if you die. In order to put off paying for this, they will find it worthwhile to subsidize your medical treatment, and they will find it worth paying even in cases where health insurance might balk. Importantly, after the contract is signed your incentives are perfectly aligned – either the event happened, and you have money in hand to do something about it, or they wish to prevent the event from happening for the same reasons you would.

In Koijen and Van Nieuwerbergh, they give the example of immunotherapies. Many cancers have treatments that work by convincing your body to attack the cancerous cells. Things like monoclonal antibodies work by attaching to proteins which cancers tend to have, but regular human cells don’t, allowing us to treat the disease in a way that does not require ingesting actual poison. These are, however, generally incredibly expensive, on the order of hundreds of thousands of dollars. Health insurance will often refuse to pay for this, and the patient will face an enormous copay in any case. Simple, standard policies, however, suggest that life insurance companies should be fully willing to pay out of their own pocket to get you healthcare, just to push the day they have to pay your decedents further into the future.

They also propose a simple way to implement this. Have the policyholder draw down their death benefit to pay for the treatment. With restrictions on what it can be spent on, such a policy is costless. The only thing standing in our way is regulation. Health insurance has a thicket of regulations that vary by state, plus constant negotiations with healthcare providers over how much they are willing to pay. It would certainly be daunting for life insurance providers to enter an entirely new line of business.