Government is what needs to be "taken out of the loop".  The healthcare insurance industry is largely the product of government interference in the free market.

Employer-sponsored healthcare programs gained popularity largely because of government-imposed wage freezes during WWII.  Since employers were prohibited by law from offering higher wages as an incentive to attract labor, they instead opted to add health coverage as part of their benefit packages.  How that came to be some sort of "moral obligation" on the part of a business owner escapes me.

The current proposals are nothing new.  President Richard Nixon, in his final State of the Union address, proposed "...a sweeping new program that will assure comprehensive health-insurance protection to millions of Americans who cannot now obtain it or afford it, with vastly improved protection against catastrophic illnesses..."  (yeah, and we all saw how well his wage and price controls worked, didn't we?)  Any proposal to overhaul the healthcare insurance system will simply be more interference by a government trying "fix" the problem by doing more of what caused it in the first place.