Well, the short answer is that the public wants three things from a healthcare system. They are, in no particular order, affordability, choice of providers, and high quality.
What’s not on that list is who runs the system. Government insured, privately insured….nada. The average patient could care less.
There are a few ideologues, mostly intending to vote for Mr. Sanders, running around insisting that private insurance must be abolished. You ask them why, and they have no idea. They mumble a few statements about “health care shouldn’t be for profit” (why not?), “the insurers are making us suffer while they make tons of profit (not….really), and then fall back to “everyone loves Medicare” (sure, but no presidential candidate is suggesting a mere extension of Medicare — — they are talking about 100% rip and replace with a new system of the same name).
The value that the private insurers bring to the table is fraud detection. They are extremely good at it, while the government is well known for “waste, fraud, and abuse” in the Medicare system. If you get rid of the private insurers, the taxpayers would probably suffer more losses from fraud than the privates were making in profits. :-(