One thing that's often overlooked is the cost of administering a billing system. If you're going to distinguish between the insured and uninsured you need a system that keeps track of who has insurance. You need paperwork (or digital equivalent). You need accounts payable staff to send invoices and chase up unpaid bills. It can, counter-intuitively, work out cheaper just not to charge anyone.

So everyone's covered unless you explicitly opt-out?