There would be a lot of complications. You’d need some way to simplify the administration, so you don’t have to submit claims to every company that ever insured you. Perhaps you’d just submit to your current company and they’d submit subordinate claims to past companies or something. The point would be to let the insurance companies fight over it without involving the patient.

You’d need a robust reinsurance market, to allow companies to lay off risks they don’t know how to manage. For example, some companies may specialize in long-term diseases like multiple sclerosis or cystic fibrosis. Conceivably, such companies might have an incentive to develop new drugs and treatments in order to reduce their long-term costs.

You’d also need some insurer of last resort, probably the federal government, to handle what happens when an insurance company goes out of business. Probably this should be some sort of FDIC-style proceeding, where other companies bid how much they want to pick up a patient’s coverage, with the government making up the difference between the failed company’s assets and the total bid package.

An interesting proposal that has never occurred to me. In a way, it would be like auto insurance or malpractice insurance. Even when the policies are discontinued, claims for events that occurred while the policy was in force are covered until up until the statute of limitations negates the possibility of a legal claim.