This idea should be well-known, not novel

A small Michigan insurer is trying a novel way to woo young, healthy people who lack health insurance: let them buy lots of coverage after they get sick.

American Community Mutual Insurance Co. is rolling out an unusual two-tier coverage plan today that would give policyholders struck by serious illness or accidents the option of adding $5 million of coverage.

Here is the article.  Here is John Cochrane on time consistent health insurance , a more radical and indeed consistent version of the same idea (you can also find this paper in Alex's excellent book Entrepreneurial Economics).  Under Cochrane's scheme, you also insure against the possibility of your premiums rising in cost, due to your illness.  In essence you are buying insurance against bad health insurance outcomes.  So if you get sick yes you can buy more insurance and yes your premiums cost more but in part you are protected against bearing all of those costs yourself.