The German model is really quite interesting, even though some aspects are extremely strange (like high income earners opting out of the public system or public servants mostly using private insurance). I like that public insurance companies still need to compete with each other on customer service etc. America is probably beyond help but I could see a system where 5% of your income HAS to go to an insurance company that you can choose gaining acceptance.

The Australian private insurance system also works like that. Private insurers have to offer pre-defined tiers with pre-defined coverage.