I don't think anyone would support a guaranteed annual income so high as to underwrite the cost of health insurance particularly if participation is not mandatory.

I can think of lots of totalitarian states posing as communistic but not one that could be remotely described as such (excepting Cuba perhaps where decent health care is provided).  China, for instance, has few social supports and health care is not one of them; Russia in theory, but not in practice, has universal health care.

The cost of any procedure in America is based on whatever the market will bear not set by the government under a single payer system.

The private sector exists for one reason only which is to make a profit for investors.  There is nothing inherently wrong with this if there is reasonable oversight and regulation however legislators, in the face of strong lobbying activity, are loathe to act.