Not sure where you get the idea that there is no competition. About every year I send out our company's program for bids. We shop the plan, we tweak it, we get varying quotes from a cross section of insurers, some who do better in certain markets, some who do better with certain groups, some who do better with certain pool sizes etc...etc... There is nothing that the government could provide that would be more cost efficient, or a better fit to our paticular group and employee profile.
WE DON'T WANT GOVERNMENT INVOLVEMENT!!!!!!!!!!!!!!!!!!!!
PS -- "Medicare - the example of a "single payer" system (government pays for healthcare)"
No! - the taxpayers pay for it